Primary 4 Mathematics Tuition | Tai Hwan Grove Weekday vs Weekend Parent Dilemma

A class maths card displays 7.486. Rounded to the nearest two decimal places it is 7.49, to the nearest one decimal place it is 7.5, and to the nearest whole number it is 7. For Tai Hwan Grove families comparing weekday and weekend Primary 4 Mathematics tuition, the diagnostic is whether the learner identifies which place to retain before looking at the deciding digit.

The thousandths six causes the hundredths eight to increase when two decimal places are needed. The hundredths eight causes the tenths four to increase when one place is needed. The tenths four keeps the ones seven unchanged when rounding to a whole number.

The updated MOE Primary 4 Mathematics syllabus covers decimals up to three decimal places and rounding to whole numbers, one decimal and two decimal places. This guide uses invented decimal cards, fully checked boundaries and later independent tasks rather than claiming real measurements or tutoring availability in the residential street.

Three correct approximations of 7.486 depend on the place requested

The number 7.486 has seven ones, four tenths, eight hundredths and six thousandths. It is the same original value regardless of how many decimal places a question asks a pupil to report.

To the nearest two decimal places, inspect the thousandths digit, six. Six is at least five, so the hundredths digit eight rounds upward to nine. The answer is 7.49.

To the nearest one decimal place, inspect the hundredths digit, eight. It makes the four tenths round upward to five tenths, giving 7.5.

To the nearest whole number, inspect the tenths digit, four. Because four is less than five, the ones digit stays seven; the answer is 7.

These are three different valid approximations of the same number. The question’s requested accuracy determines which one is appropriate, not an assumption that an answer should always keep two places.

A pupil should report rounding with language such as “approximately equal to”. The original exact decimal 7.486 has not changed value merely because the pupil wrote a shorter approximation.

A useful tutor begins by asking what “nearest whole”, “one decimal place” and “two decimal places” mean before showing the algorithm. A correct numeral obtained under repeated prompting does not yet prove independent understanding.

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Read decimal place value before rounding

Draw a chart headed Ones, Tenths, Hundredths and Thousandths. Place the digits of 7.486 into those respective columns: 7, 4, 8 and 6.

The value is seven plus four tenths plus eight hundredths plus six thousandths. Each step one place to the right represents pieces ten times smaller than the place immediately to its left.

A pupil may treat the digits 486 after the point as an unrelated whole number four hundred eighty-six. Instead, use a decimal grid or thousandths representation to show that the fractional amount is smaller than one.

The number 7.486 lies between seven and eight. Its fractional part is close to one half, but still below 7.5, which explains why it rounds down to seven to the nearest whole number.

The same number lies between 7.48 and 7.49. It is six thousandths above 7.480 but only four thousandths below 7.490, so the nearer hundredth is 7.49.

This distance explanation is useful when a pupil has memorised “five or more round up” but cannot say what the approximation measures.

The tutor should hear an independent place-value reading first. A mistake at that stage calls for a decimal chart rather than a longer sheet of rounding rules.

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Nearest two decimal places: keep hundredths, inspect thousandths

When asked for two decimal places, the last retained position is the hundredths. The digit immediately to its right is the thousandths, which controls the direction of rounding.

For 7.486, the hundredths digit is eight and the thousandths digit is six. Because six is at least five, increase the retained hundredths digit by one.

The rounded value is 7.49. The trailing thousandths digit is dropped only after it has been used to decide the direction.

A pupil who writes 7.48 has simply cut off the final six without rounding. Truncation and rounding are different operations; the nearer hundredth is 7.49.

For a boundary case such as 7.495, rounding to two decimal places gives 7.50 because the hundredths digit nine increases past nine and carries into the tenths.

A good explanation names the target place and the deciding digit. “I keep hundredths and the next digit is six, so I round up” is more meaningful than “move the decimal point”.

The answer should be shown with exactly two decimal places when that level of precision is requested, including a zero where necessary after a carrying step.

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Nearest one decimal place: keep tenths, inspect hundredths

Rounding to one decimal place retains the tenths digit. The immediately following hundredths digit determines whether the tenths remain or increase.

In 7.486, the tenths digit is four and the hundredths digit is eight. Because eight is at least five, the tenths become five, giving 7.5.

Do not compare only the thousandths six when rounding to one decimal. The first discarded place—the hundredths—is the deciding position.

A child might write 7.4 by deleting the hundredths and thousandths without checking their value. The result is a truncation rather than a correct nearest-tenth approximation.

On a number line marked 7.4 and 7.5, the original 7.486 lies very close to 7.5. The distance to 7.5 is 0.014, smaller than the distance to 7.4 of 0.086.

A decimal place-value grid can help the pupil identify which digit should change and which later digits should be omitted from the displayed rounded result.

The method transfers to other numbers: a hundredths digit of four keeps the tenths unchanged, while a hundredths digit of five or more raises it in the usual positive-decimal rounding convention.

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Nearest whole number: decide from tenths

To round 7.486 to a whole number, retain the ones digit and inspect the tenths digit immediately to its right.

The tenths digit is four. Because it is below five, keep seven as the nearest whole number: 7.486 ≈ 7.

A student may reason that the final digits eight and six look large and therefore round to eight. Those deeper places do not override the deciding tenths digit for nearest-whole rounding.

The number lies between seven and eight, with the halfway point at 7.5. Since 7.486 is below that midpoint, it is closer to seven.

For contrast, 7.586 is greater than 7.5 and rounds to eight. Only the first discarded tenths value determines the nearest whole-number direction.

A child should not apply the two-decimal result as a new original number without understanding possible double-rounding effects. Use the given full value and the requested target place directly.

The pupil’s written response should show which approximation was requested: 7.486 rounded to the nearest whole is 7, not 7.5 or 7.49.

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Rounding through nine requires carrying, not extra digits

A common challenge appears when the retained digit is nine and must increase. For example, 7.495 to two decimal places cannot become 7.410.

The hundredths digit nine is increased because the thousandths digit is five. Ten hundredths are regrouped as one tenth, so the correct rounded result is 7.50.

Another boundary case is 9.995. To two decimal places, the hundredths digit nine rounds upward, carrying through tenths and ones so the result is 10.00.

The numerical value does not become larger by a whole arbitrary amount. The rounded number is exactly the next two-decimal-place candidate closest to the original.

A tutor can illustrate this on a short number line between 7.49 and 7.50. The midpoint 7.495 rounds upward to 7.50 under the ordinary positive-number school convention.

Writing 7.5 instead of 7.50 is numerically equivalent, but the latter clearly displays the requested two decimal places. A careful response keeps the precision instruction visible.

This concept needs attention to regrouping place values. Repeating the phrase “five or more go up” without showing the carry may lead to nonsensical results when a nine is involved.

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Estimate whether each rounded answer is sensible

The original 7.486 is less than eight and greater than seven. Every rounded result should remain close to this interval rather than jump to a number such as seventy-four.

The nearest hundredth 7.49 differs from the original by 0.004, only four thousandths. An answer of 7.48 would differ by 0.006 and is therefore farther away.

The nearest tenth 7.5 differs from the original by 0.014. The alternative candidate 7.4 differs by 0.086, making 7.5 the better approximation.

The nearest whole seven differs by 0.486, while eight differs by 0.514. Seven is closer, even though the fractional digits contain an eight and six.

These distance checks are optional extensions to the basic digit rule, but they provide a reason that a child can explain rather than simply recite.

A pupil who records a correct approximation with the wrong number of decimal places should be asked which place the question requested, not simply marked as weak in arithmetic.

Use one changed number after a delay to confirm that the explanation transfers and was not memorised from the original 7.486 example.

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Distinguish rounding from deleting digits

Deleting every digit after the hundredths in 7.486 produces 7.48. That is truncating to two decimal places, not rounding to the nearest two decimal places.

The true nearest hundredth is 7.49 because the removed thousandths digit six tells us the original lies closer to 7.49 than 7.48.

The difference also appears in money notation. A system that simply cuts off digits may understate a measured quantity; the mathematical rule of rounding asks for the nearest representable value at the requested precision.

In a school question, the usual instruction “round to two decimal places” calls for the nearest value, not arbitrary deletion. The pupil should read the word “nearest” carefully.

Show the learner two candidate endpoints such as 7.48 and 7.49 on a number line, then locate 7.486 between them. This representation helps establish why the deciding digit matters.

A child who always drops the extra digit may appear accurate on examples ending in one, two, three or four. Include examples ending in six, seven, eight or nine to reveal the missing rounding step.

The tutor should keep the first wrong response and ask for a new number with a different deciding digit after the correction.

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Weekday tutoring can use a fresh decimal misconception

A weekday Primary 4 lesson may connect with a recent school decimal-place question while the learner still remembers why a digit was retained or dropped.

The family should confirm the actual classroom address before judging the journey from Tai Hwan Grove. The residential street itself is not a claim of an eduKate venue.

School dismissal, meals, enrichment, homework and bedtime determine how much attention remains for place-value precision. A rushed child may copy digits without checking the instruction.

A focused session can compare nearest whole, one decimal and two decimal places for the same original number and then give an unseen boundary case.

The tutor should ask the pupil to identify the target place and first discarded digit without being prompted on each question. That is stronger evidence than simply obtaining one correct rounded result.

A short delayed check can reveal whether the learner remembers the method independently. The original 7.486 value should not be the only assessed example.

A sustainable weekday routine protects rest and school responsibilities while providing time for accurate mathematical language.

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Weekend learning may help with decimal grids and number lines

A weekend tutorial may allow more time to build tenths, hundredths and thousandths using a place-value chart and number line.

The pupil can plot 7.486 between 7.48 and 7.49 and compare the distances to both. That gives a concrete interpretation of “nearest” beyond a verbal rounding rule.

A tutor might then present 7.495 to demonstrate a carry through a nine in the retained place. This is a useful extension when the basic rule is stable.

Weekend sport, family plans and other lessons can make an available hour unsuitable if the child is already tired. The calendar name has no universal educational advantage.

The model should lead to a written approximation at a requested number of decimal places and a short explanation of the digit that decided it.

After the model is removed, the learner should complete an unfamiliar rounding task independently and explain its answer. That is the point of the physical representation.

A new problem several days later is stronger evidence than repeating 7.486 immediately after a full guided explanation.

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Three learners may make different rounding errors

One pupil may know the place-value chart but always delete digits. Another may round correctly except when a retained nine needs carrying. A third may calculate the correct value but use the wrong target number of decimal places.

The first needs the nearest-value number line, the second needs place-value regrouping, and the third needs to identify the explicit precision instruction before calculating.

A three-pupil tutorial should collect first independent answers before anyone shares the rounded value. Otherwise one confident pupil can conceal the others’ different misconceptions.

A useful prompt might be “Which digit will you keep?”, “What does the next digit tell you?”, or “What happens when nine increases by one?”

The tutor can use different numbers for each learner while maintaining a common conceptual goal: one approximation faithful to the original value and requested place.

After hints are withdrawn, each child should face a changed number. A successful group solution cannot substitute for a later independent attempt.

Parents can ask which first decision improved and whether a delayed unseen boundary case was solved without prompts.

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Four checkpoints to make decimal rounding independent

Week one can secure the values of ones, tenths, hundredths and thousandths using written decimal cards and a place-value chart.

Week two can round familiar positive decimals to a whole number or one decimal place, naming the deciding digit before changing a retained value.

Week three can work on two decimal places and on cases with a retained nine that requires a carry, comparing answers with a short number line.

Week four can present new numbers after a delay and ask the child to choose the correct precision directly from the problem statement.

Keep a short log of the original answer, first hint, corrected explanation and later independent result. The first wrong mathematical move should guide the next practice.

If the place value is secure but carrying fails, practise that specific boundary. If the calculation is right but the number of displayed places is wrong, work on reading the instruction.

The sequence is illustrative and should adapt to real school progression rather than promise mastery within exactly four lessons.

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Thirty-four original three-decimal rounding cards with checks

These are fictitious number cards for Primary 4 Mathematics, not measurements of a physical building or local property. On every card, first identify the retained place and the next smaller deciding place, then calculate the approximate value and explain the direction. A result rounded to two decimal places is not automatically the result rounded to one decimal place.

1. Round 7.486 to three different accuracies

Independent task: a class number card contains 7.486, which has 7 as its whole-number part, 4 in the tenths place, 8 in the hundredths and 6 in the thousandths. Ask the pupil for the nearest whole, one decimal place and two decimal places without showing the completed examples. The first task is identifying which digit the instruction says to retain.

Nearest hundredth: the last retained place is hundredths and the deciding digit is the thousandths, 6. Since this digit is five or greater, the hundredths rounds upwards, with carrying when necessary. The answer to two decimal places is 7.49. This is an approximation of 7.486, not a claim that the original exact decimal has literally changed.

Nearest tenth: inspect the original hundredths digit, 8, immediately to the right of the tenths. It is five or greater, so the tenths rounds upwards. The answer to one decimal place is 7.5. Avoid simply rounding the previously written two-decimal answer again; use the given full original number and the requested place.

Nearest whole number: the deciding digit is the original tenths, 4. Because it is below five, the nearest whole number is 7. The pupil can check that the original 7.486 lies close to the stated integer and that this instruction differs from reporting one or two decimal places.

Reasonableness check: the nearest-hundredth approximation 7.49 is exactly 4 thousandths away from 7.486, no greater than five thousandths under the ordinary positive-number convention. Ask how this would change if the thousandths digit were one lower or one higher, where that remains a valid digit. A new deciding digit provides more reliable evidence than copying these completed numerals.

2. Round 7.485 to three different accuracies

Independent task: a class number card contains 7.485, which has 7 as its whole-number part, 4 in the tenths place, 8 in the hundredths and 5 in the thousandths. Ask the pupil for the nearest whole, one decimal place and two decimal places without showing the completed examples. The first task is identifying which digit the instruction says to retain.

Nearest hundredth: the last retained place is hundredths and the deciding digit is the thousandths, 5. Since this digit is five or greater, the hundredths rounds upwards, with carrying when necessary. The answer to two decimal places is 7.49. This is an approximation of 7.485, not a claim that the original exact decimal has literally changed.

Nearest tenth: inspect the original hundredths digit, 8, immediately to the right of the tenths. It is five or greater, so the tenths rounds upwards. The answer to one decimal place is 7.5. Avoid simply rounding the previously written two-decimal answer again; use the given full original number and the requested place.

Nearest whole number: the deciding digit is the original tenths, 4. Because it is below five, the nearest whole number is 7. The pupil can check that the original 7.485 lies close to the stated integer and that this instruction differs from reporting one or two decimal places.

Reasonableness check: the nearest-hundredth approximation 7.49 is exactly 5 thousandths away from 7.485, no greater than five thousandths under the ordinary positive-number convention. Ask how this would change if the thousandths digit were one lower or one higher, where that remains a valid digit. A new deciding digit provides more reliable evidence than copying these completed numerals.

3. Round 7.484 to three different accuracies

Independent task: a class number card contains 7.484, which has 7 as its whole-number part, 4 in the tenths place, 8 in the hundredths and 4 in the thousandths. Ask the pupil for the nearest whole, one decimal place and two decimal places without showing the completed examples. The first task is identifying which digit the instruction says to retain.

Nearest hundredth: the last retained place is hundredths and the deciding digit is the thousandths, 4. Since this digit is less than five, the hundredths remains unchanged. The answer to two decimal places is 7.48. This is an approximation of 7.484, not a claim that the original exact decimal has literally changed.

Nearest tenth: inspect the original hundredths digit, 8, immediately to the right of the tenths. It is five or greater, so the tenths rounds upwards. The answer to one decimal place is 7.5. Avoid simply rounding the previously written two-decimal answer again; use the given full original number and the requested place.

Nearest whole number: the deciding digit is the original tenths, 4. Because it is below five, the nearest whole number is 7. The pupil can check that the original 7.484 lies close to the stated integer and that this instruction differs from reporting one or two decimal places.

Reasonableness check: the nearest-hundredth approximation 7.48 is exactly 4 thousandths away from 7.484, no greater than five thousandths under the ordinary positive-number convention. Ask how this would change if the thousandths digit were one lower or one higher, where that remains a valid digit. A new deciding digit provides more reliable evidence than copying these completed numerals.

4. Round 7.495 to three different accuracies

Independent task: a class number card contains 7.495, which has 7 as its whole-number part, 4 in the tenths place, 9 in the hundredths and 5 in the thousandths. Ask the pupil for the nearest whole, one decimal place and two decimal places without showing the completed examples. The first task is identifying which digit the instruction says to retain.

Nearest hundredth: the last retained place is hundredths and the deciding digit is the thousandths, 5. Since this digit is five or greater, the hundredths rounds upwards, with carrying when necessary. The answer to two decimal places is 7.50. This is an approximation of 7.495, not a claim that the original exact decimal has literally changed.

Nearest tenth: inspect the original hundredths digit, 9, immediately to the right of the tenths. It is five or greater, so the tenths rounds upwards. The answer to one decimal place is 7.5. Avoid simply rounding the previously written two-decimal answer again; use the given full original number and the requested place.

Nearest whole number: the deciding digit is the original tenths, 4. Because it is below five, the nearest whole number is 7. The pupil can check that the original 7.495 lies close to the stated integer and that this instruction differs from reporting one or two decimal places.

Reasonableness check: the nearest-hundredth approximation 7.50 is exactly 5 thousandths away from 7.495, no greater than five thousandths under the ordinary positive-number convention. Ask how this would change if the thousandths digit were one lower or one higher, where that remains a valid digit. A new deciding digit provides more reliable evidence than copying these completed numerals.

5. Round 7.999 to three different accuracies

Independent task: a class number card contains 7.999, which has 7 as its whole-number part, 9 in the tenths place, 9 in the hundredths and 9 in the thousandths. Ask the pupil for the nearest whole, one decimal place and two decimal places without showing the completed examples. The first task is identifying which digit the instruction says to retain.

Nearest hundredth: the last retained place is hundredths and the deciding digit is the thousandths, 9. Since this digit is five or greater, the hundredths rounds upwards, with carrying when necessary. The answer to two decimal places is 8.00. This is an approximation of 7.999, not a claim that the original exact decimal has literally changed.

Nearest tenth: inspect the original hundredths digit, 9, immediately to the right of the tenths. It is five or greater, so the tenths rounds upwards. The answer to one decimal place is 8.0. Avoid simply rounding the previously written two-decimal answer again; use the given full original number and the requested place.

Nearest whole number: the deciding digit is the original tenths, 9. Because it is at least five, the nearest whole number is 8. The pupil can check that the original 7.999 lies close to the stated integer and that this instruction differs from reporting one or two decimal places.

Reasonableness check: the nearest-hundredth approximation 8.00 is exactly 1 thousandths away from 7.999, no greater than five thousandths under the ordinary positive-number convention. Ask how this would change if the thousandths digit were one lower or one higher, where that remains a valid digit. A new deciding digit provides more reliable evidence than copying these completed numerals.

6. Round 7.004 to three different accuracies

Independent task: a class number card contains 7.004, which has 7 as its whole-number part, 0 in the tenths place, 0 in the hundredths and 4 in the thousandths. Ask the pupil for the nearest whole, one decimal place and two decimal places without showing the completed examples. The first task is identifying which digit the instruction says to retain.

Nearest hundredth: the last retained place is hundredths and the deciding digit is the thousandths, 4. Since this digit is less than five, the hundredths remains unchanged. The answer to two decimal places is 7.00. This is an approximation of 7.004, not a claim that the original exact decimal has literally changed.

Nearest tenth: inspect the original hundredths digit, 0, immediately to the right of the tenths. It is below five, so the tenths stays at its existing value. The answer to one decimal place is 7.0. Avoid simply rounding the previously written two-decimal answer again; use the given full original number and the requested place.

Nearest whole number: the deciding digit is the original tenths, 0. Because it is below five, the nearest whole number is 7. The pupil can check that the original 7.004 lies close to the stated integer and that this instruction differs from reporting one or two decimal places.

Reasonableness check: the nearest-hundredth approximation 7.00 is exactly 4 thousandths away from 7.004, no greater than five thousandths under the ordinary positive-number convention. Ask how this would change if the thousandths digit were one lower or one higher, where that remains a valid digit. A new deciding digit provides more reliable evidence than copying these completed numerals.

7. Round 0.046 to three different accuracies

Independent task: a class number card contains 0.046, which has 0 as its whole-number part, 0 in the tenths place, 4 in the hundredths and 6 in the thousandths. Ask the pupil for the nearest whole, one decimal place and two decimal places without showing the completed examples. The first task is identifying which digit the instruction says to retain.

Nearest hundredth: the last retained place is hundredths and the deciding digit is the thousandths, 6. Since this digit is five or greater, the hundredths rounds upwards, with carrying when necessary. The answer to two decimal places is 0.05. This is an approximation of 0.046, not a claim that the original exact decimal has literally changed.

Nearest tenth: inspect the original hundredths digit, 4, immediately to the right of the tenths. It is below five, so the tenths stays at its existing value. The answer to one decimal place is 0.0. Avoid simply rounding the previously written two-decimal answer again; use the given full original number and the requested place.

Nearest whole number: the deciding digit is the original tenths, 0. Because it is below five, the nearest whole number is 0. The pupil can check that the original 0.046 lies close to the stated integer and that this instruction differs from reporting one or two decimal places.

Reasonableness check: the nearest-hundredth approximation 0.05 is exactly 4 thousandths away from 0.046, no greater than five thousandths under the ordinary positive-number convention. Ask how this would change if the thousandths digit were one lower or one higher, where that remains a valid digit. A new deciding digit provides more reliable evidence than copying these completed numerals.

8. Round 0.045 to three different accuracies

Independent task: a class number card contains 0.045, which has 0 as its whole-number part, 0 in the tenths place, 4 in the hundredths and 5 in the thousandths. Ask the pupil for the nearest whole, one decimal place and two decimal places without showing the completed examples. The first task is identifying which digit the instruction says to retain.

Nearest hundredth: the last retained place is hundredths and the deciding digit is the thousandths, 5. Since this digit is five or greater, the hundredths rounds upwards, with carrying when necessary. The answer to two decimal places is 0.05. This is an approximation of 0.045, not a claim that the original exact decimal has literally changed.

Nearest tenth: inspect the original hundredths digit, 4, immediately to the right of the tenths. It is below five, so the tenths stays at its existing value. The answer to one decimal place is 0.0. Avoid simply rounding the previously written two-decimal answer again; use the given full original number and the requested place.

Nearest whole number: the deciding digit is the original tenths, 0. Because it is below five, the nearest whole number is 0. The pupil can check that the original 0.045 lies close to the stated integer and that this instruction differs from reporting one or two decimal places.

Reasonableness check: the nearest-hundredth approximation 0.05 is exactly 5 thousandths away from 0.045, no greater than five thousandths under the ordinary positive-number convention. Ask how this would change if the thousandths digit were one lower or one higher, where that remains a valid digit. A new deciding digit provides more reliable evidence than copying these completed numerals.

9. Round 0.044 to three different accuracies

Independent task: a class number card contains 0.044, which has 0 as its whole-number part, 0 in the tenths place, 4 in the hundredths and 4 in the thousandths. Ask the pupil for the nearest whole, one decimal place and two decimal places without showing the completed examples. The first task is identifying which digit the instruction says to retain.

Nearest hundredth: the last retained place is hundredths and the deciding digit is the thousandths, 4. Since this digit is less than five, the hundredths remains unchanged. The answer to two decimal places is 0.04. This is an approximation of 0.044, not a claim that the original exact decimal has literally changed.

Nearest tenth: inspect the original hundredths digit, 4, immediately to the right of the tenths. It is below five, so the tenths stays at its existing value. The answer to one decimal place is 0.0. Avoid simply rounding the previously written two-decimal answer again; use the given full original number and the requested place.

Nearest whole number: the deciding digit is the original tenths, 0. Because it is below five, the nearest whole number is 0. The pupil can check that the original 0.044 lies close to the stated integer and that this instruction differs from reporting one or two decimal places.

Reasonableness check: the nearest-hundredth approximation 0.04 is exactly 4 thousandths away from 0.044, no greater than five thousandths under the ordinary positive-number convention. Ask how this would change if the thousandths digit were one lower or one higher, where that remains a valid digit. A new deciding digit provides more reliable evidence than copying these completed numerals.

10. Round 3.275 to three different accuracies

Independent task: a class number card contains 3.275, which has 3 as its whole-number part, 2 in the tenths place, 7 in the hundredths and 5 in the thousandths. Ask the pupil for the nearest whole, one decimal place and two decimal places without showing the completed examples. The first task is identifying which digit the instruction says to retain.

Nearest hundredth: the last retained place is hundredths and the deciding digit is the thousandths, 5. Since this digit is five or greater, the hundredths rounds upwards, with carrying when necessary. The answer to two decimal places is 3.28. This is an approximation of 3.275, not a claim that the original exact decimal has literally changed.

Nearest tenth: inspect the original hundredths digit, 7, immediately to the right of the tenths. It is five or greater, so the tenths rounds upwards. The answer to one decimal place is 3.3. Avoid simply rounding the previously written two-decimal answer again; use the given full original number and the requested place.

Nearest whole number: the deciding digit is the original tenths, 2. Because it is below five, the nearest whole number is 3. The pupil can check that the original 3.275 lies close to the stated integer and that this instruction differs from reporting one or two decimal places.

Reasonableness check: the nearest-hundredth approximation 3.28 is exactly 5 thousandths away from 3.275, no greater than five thousandths under the ordinary positive-number convention. Ask how this would change if the thousandths digit were one lower or one higher, where that remains a valid digit. A new deciding digit provides more reliable evidence than copying these completed numerals.

11. Round 3.274 to three different accuracies

Independent task: a class number card contains 3.274, which has 3 as its whole-number part, 2 in the tenths place, 7 in the hundredths and 4 in the thousandths. Ask the pupil for the nearest whole, one decimal place and two decimal places without showing the completed examples. The first task is identifying which digit the instruction says to retain.

Nearest hundredth: the last retained place is hundredths and the deciding digit is the thousandths, 4. Since this digit is less than five, the hundredths remains unchanged. The answer to two decimal places is 3.27. This is an approximation of 3.274, not a claim that the original exact decimal has literally changed.

Nearest tenth: inspect the original hundredths digit, 7, immediately to the right of the tenths. It is five or greater, so the tenths rounds upwards. The answer to one decimal place is 3.3. Avoid simply rounding the previously written two-decimal answer again; use the given full original number and the requested place.

Nearest whole number: the deciding digit is the original tenths, 2. Because it is below five, the nearest whole number is 3. The pupil can check that the original 3.274 lies close to the stated integer and that this instruction differs from reporting one or two decimal places.

Reasonableness check: the nearest-hundredth approximation 3.27 is exactly 4 thousandths away from 3.274, no greater than five thousandths under the ordinary positive-number convention. Ask how this would change if the thousandths digit were one lower or one higher, where that remains a valid digit. A new deciding digit provides more reliable evidence than copying these completed numerals.

12. Round 3.295 to three different accuracies

Independent task: a class number card contains 3.295, which has 3 as its whole-number part, 2 in the tenths place, 9 in the hundredths and 5 in the thousandths. Ask the pupil for the nearest whole, one decimal place and two decimal places without showing the completed examples. The first task is identifying which digit the instruction says to retain.

Nearest hundredth: the last retained place is hundredths and the deciding digit is the thousandths, 5. Since this digit is five or greater, the hundredths rounds upwards, with carrying when necessary. The answer to two decimal places is 3.30. This is an approximation of 3.295, not a claim that the original exact decimal has literally changed.

Nearest tenth: inspect the original hundredths digit, 9, immediately to the right of the tenths. It is five or greater, so the tenths rounds upwards. The answer to one decimal place is 3.3. Avoid simply rounding the previously written two-decimal answer again; use the given full original number and the requested place.

Nearest whole number: the deciding digit is the original tenths, 2. Because it is below five, the nearest whole number is 3. The pupil can check that the original 3.295 lies close to the stated integer and that this instruction differs from reporting one or two decimal places.

Reasonableness check: the nearest-hundredth approximation 3.30 is exactly 5 thousandths away from 3.295, no greater than five thousandths under the ordinary positive-number convention. Ask how this would change if the thousandths digit were one lower or one higher, where that remains a valid digit. A new deciding digit provides more reliable evidence than copying these completed numerals.

13. Round 6.739 to three different accuracies

Independent task: a class number card contains 6.739, which has 6 as its whole-number part, 7 in the tenths place, 3 in the hundredths and 9 in the thousandths. Ask the pupil for the nearest whole, one decimal place and two decimal places without showing the completed examples. The first task is identifying which digit the instruction says to retain.

Nearest hundredth: the last retained place is hundredths and the deciding digit is the thousandths, 9. Since this digit is five or greater, the hundredths rounds upwards, with carrying when necessary. The answer to two decimal places is 6.74. This is an approximation of 6.739, not a claim that the original exact decimal has literally changed.

Nearest tenth: inspect the original hundredths digit, 3, immediately to the right of the tenths. It is below five, so the tenths stays at its existing value. The answer to one decimal place is 6.7. Avoid simply rounding the previously written two-decimal answer again; use the given full original number and the requested place.

Nearest whole number: the deciding digit is the original tenths, 7. Because it is at least five, the nearest whole number is 7. The pupil can check that the original 6.739 lies close to the stated integer and that this instruction differs from reporting one or two decimal places.

Reasonableness check: the nearest-hundredth approximation 6.74 is exactly 1 thousandths away from 6.739, no greater than five thousandths under the ordinary positive-number convention. Ask how this would change if the thousandths digit were one lower or one higher, where that remains a valid digit. A new deciding digit provides more reliable evidence than copying these completed numerals.

14. Round 4.665 to three different accuracies

Independent task: a class number card contains 4.665, which has 4 as its whole-number part, 6 in the tenths place, 6 in the hundredths and 5 in the thousandths. Ask the pupil for the nearest whole, one decimal place and two decimal places without showing the completed examples. The first task is identifying which digit the instruction says to retain.

Nearest hundredth: the last retained place is hundredths and the deciding digit is the thousandths, 5. Since this digit is five or greater, the hundredths rounds upwards, with carrying when necessary. The answer to two decimal places is 4.67. This is an approximation of 4.665, not a claim that the original exact decimal has literally changed.

Nearest tenth: inspect the original hundredths digit, 6, immediately to the right of the tenths. It is five or greater, so the tenths rounds upwards. The answer to one decimal place is 4.7. Avoid simply rounding the previously written two-decimal answer again; use the given full original number and the requested place.

Nearest whole number: the deciding digit is the original tenths, 6. Because it is at least five, the nearest whole number is 5. The pupil can check that the original 4.665 lies close to the stated integer and that this instruction differs from reporting one or two decimal places.

Reasonableness check: the nearest-hundredth approximation 4.67 is exactly 5 thousandths away from 4.665, no greater than five thousandths under the ordinary positive-number convention. Ask how this would change if the thousandths digit were one lower or one higher, where that remains a valid digit. A new deciding digit provides more reliable evidence than copying these completed numerals.

15. Round 4.664 to three different accuracies

Independent task: a class number card contains 4.664, which has 4 as its whole-number part, 6 in the tenths place, 6 in the hundredths and 4 in the thousandths. Ask the pupil for the nearest whole, one decimal place and two decimal places without showing the completed examples. The first task is identifying which digit the instruction says to retain.

Nearest hundredth: the last retained place is hundredths and the deciding digit is the thousandths, 4. Since this digit is less than five, the hundredths remains unchanged. The answer to two decimal places is 4.66. This is an approximation of 4.664, not a claim that the original exact decimal has literally changed.

Nearest tenth: inspect the original hundredths digit, 6, immediately to the right of the tenths. It is five or greater, so the tenths rounds upwards. The answer to one decimal place is 4.7. Avoid simply rounding the previously written two-decimal answer again; use the given full original number and the requested place.

Nearest whole number: the deciding digit is the original tenths, 6. Because it is at least five, the nearest whole number is 5. The pupil can check that the original 4.664 lies close to the stated integer and that this instruction differs from reporting one or two decimal places.

Reasonableness check: the nearest-hundredth approximation 4.66 is exactly 4 thousandths away from 4.664, no greater than five thousandths under the ordinary positive-number convention. Ask how this would change if the thousandths digit were one lower or one higher, where that remains a valid digit. A new deciding digit provides more reliable evidence than copying these completed numerals.

16. Round 8.054 to three different accuracies

Independent task: a class number card contains 8.054, which has 8 as its whole-number part, 0 in the tenths place, 5 in the hundredths and 4 in the thousandths. Ask the pupil for the nearest whole, one decimal place and two decimal places without showing the completed examples. The first task is identifying which digit the instruction says to retain.

Nearest hundredth: the last retained place is hundredths and the deciding digit is the thousandths, 4. Since this digit is less than five, the hundredths remains unchanged. The answer to two decimal places is 8.05. This is an approximation of 8.054, not a claim that the original exact decimal has literally changed.

Nearest tenth: inspect the original hundredths digit, 5, immediately to the right of the tenths. It is five or greater, so the tenths rounds upwards. The answer to one decimal place is 8.1. Avoid simply rounding the previously written two-decimal answer again; use the given full original number and the requested place.

Nearest whole number: the deciding digit is the original tenths, 0. Because it is below five, the nearest whole number is 8. The pupil can check that the original 8.054 lies close to the stated integer and that this instruction differs from reporting one or two decimal places.

Reasonableness check: the nearest-hundredth approximation 8.05 is exactly 4 thousandths away from 8.054, no greater than five thousandths under the ordinary positive-number convention. Ask how this would change if the thousandths digit were one lower or one higher, where that remains a valid digit. A new deciding digit provides more reliable evidence than copying these completed numerals.

17. Round 8.055 to three different accuracies

Independent task: a class number card contains 8.055, which has 8 as its whole-number part, 0 in the tenths place, 5 in the hundredths and 5 in the thousandths. Ask the pupil for the nearest whole, one decimal place and two decimal places without showing the completed examples. The first task is identifying which digit the instruction says to retain.

Nearest hundredth: the last retained place is hundredths and the deciding digit is the thousandths, 5. Since this digit is five or greater, the hundredths rounds upwards, with carrying when necessary. The answer to two decimal places is 8.06. This is an approximation of 8.055, not a claim that the original exact decimal has literally changed.

Nearest tenth: inspect the original hundredths digit, 5, immediately to the right of the tenths. It is five or greater, so the tenths rounds upwards. The answer to one decimal place is 8.1. Avoid simply rounding the previously written two-decimal answer again; use the given full original number and the requested place.

Nearest whole number: the deciding digit is the original tenths, 0. Because it is below five, the nearest whole number is 8. The pupil can check that the original 8.055 lies close to the stated integer and that this instruction differs from reporting one or two decimal places.

Reasonableness check: the nearest-hundredth approximation 8.06 is exactly 5 thousandths away from 8.055, no greater than five thousandths under the ordinary positive-number convention. Ask how this would change if the thousandths digit were one lower or one higher, where that remains a valid digit. A new deciding digit provides more reliable evidence than copying these completed numerals.

18. Round 9.995 to three different accuracies

Independent task: a class number card contains 9.995, which has 9 as its whole-number part, 9 in the tenths place, 9 in the hundredths and 5 in the thousandths. Ask the pupil for the nearest whole, one decimal place and two decimal places without showing the completed examples. The first task is identifying which digit the instruction says to retain.

Nearest hundredth: the last retained place is hundredths and the deciding digit is the thousandths, 5. Since this digit is five or greater, the hundredths rounds upwards, with carrying when necessary. The answer to two decimal places is 10.00. This is an approximation of 9.995, not a claim that the original exact decimal has literally changed.

Nearest tenth: inspect the original hundredths digit, 9, immediately to the right of the tenths. It is five or greater, so the tenths rounds upwards. The answer to one decimal place is 10.0. Avoid simply rounding the previously written two-decimal answer again; use the given full original number and the requested place.

Nearest whole number: the deciding digit is the original tenths, 9. Because it is at least five, the nearest whole number is 10. The pupil can check that the original 9.995 lies close to the stated integer and that this instruction differs from reporting one or two decimal places.

Reasonableness check: the nearest-hundredth approximation 10.00 is exactly 5 thousandths away from 9.995, no greater than five thousandths under the ordinary positive-number convention. Ask how this would change if the thousandths digit were one lower or one higher, where that remains a valid digit. A new deciding digit provides more reliable evidence than copying these completed numerals.

19. Round 12.345 to three different accuracies

Independent task: a class number card contains 12.345, which has 12 as its whole-number part, 3 in the tenths place, 4 in the hundredths and 5 in the thousandths. Ask the pupil for the nearest whole, one decimal place and two decimal places without showing the completed examples. The first task is identifying which digit the instruction says to retain.

Nearest hundredth: the last retained place is hundredths and the deciding digit is the thousandths, 5. Since this digit is five or greater, the hundredths rounds upwards, with carrying when necessary. The answer to two decimal places is 12.35. This is an approximation of 12.345, not a claim that the original exact decimal has literally changed.

Nearest tenth: inspect the original hundredths digit, 4, immediately to the right of the tenths. It is below five, so the tenths stays at its existing value. The answer to one decimal place is 12.3. Avoid simply rounding the previously written two-decimal answer again; use the given full original number and the requested place.

Nearest whole number: the deciding digit is the original tenths, 3. Because it is below five, the nearest whole number is 12. The pupil can check that the original 12.345 lies close to the stated integer and that this instruction differs from reporting one or two decimal places.

Reasonableness check: the nearest-hundredth approximation 12.35 is exactly 5 thousandths away from 12.345, no greater than five thousandths under the ordinary positive-number convention. Ask how this would change if the thousandths digit were one lower or one higher, where that remains a valid digit. A new deciding digit provides more reliable evidence than copying these completed numerals.

20. Round 15.075 to three different accuracies

Independent task: a class number card contains 15.075, which has 15 as its whole-number part, 0 in the tenths place, 7 in the hundredths and 5 in the thousandths. Ask the pupil for the nearest whole, one decimal place and two decimal places without showing the completed examples. The first task is identifying which digit the instruction says to retain.

Nearest hundredth: the last retained place is hundredths and the deciding digit is the thousandths, 5. Since this digit is five or greater, the hundredths rounds upwards, with carrying when necessary. The answer to two decimal places is 15.08. This is an approximation of 15.075, not a claim that the original exact decimal has literally changed.

Nearest tenth: inspect the original hundredths digit, 7, immediately to the right of the tenths. It is five or greater, so the tenths rounds upwards. The answer to one decimal place is 15.1. Avoid simply rounding the previously written two-decimal answer again; use the given full original number and the requested place.

Nearest whole number: the deciding digit is the original tenths, 0. Because it is below five, the nearest whole number is 15. The pupil can check that the original 15.075 lies close to the stated integer and that this instruction differs from reporting one or two decimal places.

Reasonableness check: the nearest-hundredth approximation 15.08 is exactly 5 thousandths away from 15.075, no greater than five thousandths under the ordinary positive-number convention. Ask how this would change if the thousandths digit were one lower or one higher, where that remains a valid digit. A new deciding digit provides more reliable evidence than copying these completed numerals.

21. Round 2.999 to three different accuracies

Independent task: a class number card contains 2.999, which has 2 as its whole-number part, 9 in the tenths place, 9 in the hundredths and 9 in the thousandths. Ask the pupil for the nearest whole, one decimal place and two decimal places without showing the completed examples. The first task is identifying which digit the instruction says to retain.

Nearest hundredth: the last retained place is hundredths and the deciding digit is the thousandths, 9. Since this digit is five or greater, the hundredths rounds upwards, with carrying when necessary. The answer to two decimal places is 3.00. This is an approximation of 2.999, not a claim that the original exact decimal has literally changed.

Nearest tenth: inspect the original hundredths digit, 9, immediately to the right of the tenths. It is five or greater, so the tenths rounds upwards. The answer to one decimal place is 3.0. Avoid simply rounding the previously written two-decimal answer again; use the given full original number and the requested place.

Nearest whole number: the deciding digit is the original tenths, 9. Because it is at least five, the nearest whole number is 3. The pupil can check that the original 2.999 lies close to the stated integer and that this instruction differs from reporting one or two decimal places.

Reasonableness check: the nearest-hundredth approximation 3.00 is exactly 1 thousandths away from 2.999, no greater than five thousandths under the ordinary positive-number convention. Ask how this would change if the thousandths digit were one lower or one higher, where that remains a valid digit. A new deciding digit provides more reliable evidence than copying these completed numerals.

22. Round 3.005 to three different accuracies

Independent task: a class number card contains 3.005, which has 3 as its whole-number part, 0 in the tenths place, 0 in the hundredths and 5 in the thousandths. Ask the pupil for the nearest whole, one decimal place and two decimal places without showing the completed examples. The first task is identifying which digit the instruction says to retain.

Nearest hundredth: the last retained place is hundredths and the deciding digit is the thousandths, 5. Since this digit is five or greater, the hundredths rounds upwards, with carrying when necessary. The answer to two decimal places is 3.01. This is an approximation of 3.005, not a claim that the original exact decimal has literally changed.

Nearest tenth: inspect the original hundredths digit, 0, immediately to the right of the tenths. It is below five, so the tenths stays at its existing value. The answer to one decimal place is 3.0. Avoid simply rounding the previously written two-decimal answer again; use the given full original number and the requested place.

Nearest whole number: the deciding digit is the original tenths, 0. Because it is below five, the nearest whole number is 3. The pupil can check that the original 3.005 lies close to the stated integer and that this instruction differs from reporting one or two decimal places.

Reasonableness check: the nearest-hundredth approximation 3.01 is exactly 5 thousandths away from 3.005, no greater than five thousandths under the ordinary positive-number convention. Ask how this would change if the thousandths digit were one lower or one higher, where that remains a valid digit. A new deciding digit provides more reliable evidence than copying these completed numerals.

23. Round 0.995 to three different accuracies

Independent task: a class number card contains 0.995, which has 0 as its whole-number part, 9 in the tenths place, 9 in the hundredths and 5 in the thousandths. Ask the pupil for the nearest whole, one decimal place and two decimal places without showing the completed examples. The first task is identifying which digit the instruction says to retain.

Nearest hundredth: the last retained place is hundredths and the deciding digit is the thousandths, 5. Since this digit is five or greater, the hundredths rounds upwards, with carrying when necessary. The answer to two decimal places is 1.00. This is an approximation of 0.995, not a claim that the original exact decimal has literally changed.

Nearest tenth: inspect the original hundredths digit, 9, immediately to the right of the tenths. It is five or greater, so the tenths rounds upwards. The answer to one decimal place is 1.0. Avoid simply rounding the previously written two-decimal answer again; use the given full original number and the requested place.

Nearest whole number: the deciding digit is the original tenths, 9. Because it is at least five, the nearest whole number is 1. The pupil can check that the original 0.995 lies close to the stated integer and that this instruction differs from reporting one or two decimal places.

Reasonableness check: the nearest-hundredth approximation 1.00 is exactly 5 thousandths away from 0.995, no greater than five thousandths under the ordinary positive-number convention. Ask how this would change if the thousandths digit were one lower or one higher, where that remains a valid digit. A new deciding digit provides more reliable evidence than copying these completed numerals.

24. Round 1.999 to three different accuracies

Independent task: a class number card contains 1.999, which has 1 as its whole-number part, 9 in the tenths place, 9 in the hundredths and 9 in the thousandths. Ask the pupil for the nearest whole, one decimal place and two decimal places without showing the completed examples. The first task is identifying which digit the instruction says to retain.

Nearest hundredth: the last retained place is hundredths and the deciding digit is the thousandths, 9. Since this digit is five or greater, the hundredths rounds upwards, with carrying when necessary. The answer to two decimal places is 2.00. This is an approximation of 1.999, not a claim that the original exact decimal has literally changed.

Nearest tenth: inspect the original hundredths digit, 9, immediately to the right of the tenths. It is five or greater, so the tenths rounds upwards. The answer to one decimal place is 2.0. Avoid simply rounding the previously written two-decimal answer again; use the given full original number and the requested place.

Nearest whole number: the deciding digit is the original tenths, 9. Because it is at least five, the nearest whole number is 2. The pupil can check that the original 1.999 lies close to the stated integer and that this instruction differs from reporting one or two decimal places.

Reasonableness check: the nearest-hundredth approximation 2.00 is exactly 1 thousandths away from 1.999, no greater than five thousandths under the ordinary positive-number convention. Ask how this would change if the thousandths digit were one lower or one higher, where that remains a valid digit. A new deciding digit provides more reliable evidence than copying these completed numerals.

25. Round 5.555 to three different accuracies

Independent task: a class number card contains 5.555, which has 5 as its whole-number part, 5 in the tenths place, 5 in the hundredths and 5 in the thousandths. Ask the pupil for the nearest whole, one decimal place and two decimal places without showing the completed examples. The first task is identifying which digit the instruction says to retain.

Nearest hundredth: the last retained place is hundredths and the deciding digit is the thousandths, 5. Since this digit is five or greater, the hundredths rounds upwards, with carrying when necessary. The answer to two decimal places is 5.56. This is an approximation of 5.555, not a claim that the original exact decimal has literally changed.

Nearest tenth: inspect the original hundredths digit, 5, immediately to the right of the tenths. It is five or greater, so the tenths rounds upwards. The answer to one decimal place is 5.6. Avoid simply rounding the previously written two-decimal answer again; use the given full original number and the requested place.

Nearest whole number: the deciding digit is the original tenths, 5. Because it is at least five, the nearest whole number is 6. The pupil can check that the original 5.555 lies close to the stated integer and that this instruction differs from reporting one or two decimal places.

Reasonableness check: the nearest-hundredth approximation 5.56 is exactly 5 thousandths away from 5.555, no greater than five thousandths under the ordinary positive-number convention. Ask how this would change if the thousandths digit were one lower or one higher, where that remains a valid digit. A new deciding digit provides more reliable evidence than copying these completed numerals.

26. Round 2.105 to three different accuracies

Independent task: a class number card contains 2.105, which has 2 as its whole-number part, 1 in the tenths place, 0 in the hundredths and 5 in the thousandths. Ask the pupil for the nearest whole, one decimal place and two decimal places without showing the completed examples. The first task is identifying which digit the instruction says to retain.

Nearest hundredth: the last retained place is hundredths and the deciding digit is the thousandths, 5. Since this digit is five or greater, the hundredths rounds upwards, with carrying when necessary. The answer to two decimal places is 2.11. This is an approximation of 2.105, not a claim that the original exact decimal has literally changed.

Nearest tenth: inspect the original hundredths digit, 0, immediately to the right of the tenths. It is below five, so the tenths stays at its existing value. The answer to one decimal place is 2.1. Avoid simply rounding the previously written two-decimal answer again; use the given full original number and the requested place.

Nearest whole number: the deciding digit is the original tenths, 1. Because it is below five, the nearest whole number is 2. The pupil can check that the original 2.105 lies close to the stated integer and that this instruction differs from reporting one or two decimal places.

Reasonableness check: the nearest-hundredth approximation 2.11 is exactly 5 thousandths away from 2.105, no greater than five thousandths under the ordinary positive-number convention. Ask how this would change if the thousandths digit were one lower or one higher, where that remains a valid digit. A new deciding digit provides more reliable evidence than copying these completed numerals.

27. Round 7.105 to three different accuracies

Independent task: a class number card contains 7.105, which has 7 as its whole-number part, 1 in the tenths place, 0 in the hundredths and 5 in the thousandths. Ask the pupil for the nearest whole, one decimal place and two decimal places without showing the completed examples. The first task is identifying which digit the instruction says to retain.

Nearest hundredth: the last retained place is hundredths and the deciding digit is the thousandths, 5. Since this digit is five or greater, the hundredths rounds upwards, with carrying when necessary. The answer to two decimal places is 7.11. This is an approximation of 7.105, not a claim that the original exact decimal has literally changed.

Nearest tenth: inspect the original hundredths digit, 0, immediately to the right of the tenths. It is below five, so the tenths stays at its existing value. The answer to one decimal place is 7.1. Avoid simply rounding the previously written two-decimal answer again; use the given full original number and the requested place.

Nearest whole number: the deciding digit is the original tenths, 1. Because it is below five, the nearest whole number is 7. The pupil can check that the original 7.105 lies close to the stated integer and that this instruction differs from reporting one or two decimal places.

Reasonableness check: the nearest-hundredth approximation 7.11 is exactly 5 thousandths away from 7.105, no greater than five thousandths under the ordinary positive-number convention. Ask how this would change if the thousandths digit were one lower or one higher, where that remains a valid digit. A new deciding digit provides more reliable evidence than copying these completed numerals.

28. Round 8.365 to three different accuracies

Independent task: a class number card contains 8.365, which has 8 as its whole-number part, 3 in the tenths place, 6 in the hundredths and 5 in the thousandths. Ask the pupil for the nearest whole, one decimal place and two decimal places without showing the completed examples. The first task is identifying which digit the instruction says to retain.

Nearest hundredth: the last retained place is hundredths and the deciding digit is the thousandths, 5. Since this digit is five or greater, the hundredths rounds upwards, with carrying when necessary. The answer to two decimal places is 8.37. This is an approximation of 8.365, not a claim that the original exact decimal has literally changed.

Nearest tenth: inspect the original hundredths digit, 6, immediately to the right of the tenths. It is five or greater, so the tenths rounds upwards. The answer to one decimal place is 8.4. Avoid simply rounding the previously written two-decimal answer again; use the given full original number and the requested place.

Nearest whole number: the deciding digit is the original tenths, 3. Because it is below five, the nearest whole number is 8. The pupil can check that the original 8.365 lies close to the stated integer and that this instruction differs from reporting one or two decimal places.

Reasonableness check: the nearest-hundredth approximation 8.37 is exactly 5 thousandths away from 8.365, no greater than five thousandths under the ordinary positive-number convention. Ask how this would change if the thousandths digit were one lower or one higher, where that remains a valid digit. A new deciding digit provides more reliable evidence than copying these completed numerals.

29. Round 4.999 to three different accuracies

Independent task: a class number card contains 4.999, which has 4 as its whole-number part, 9 in the tenths place, 9 in the hundredths and 9 in the thousandths. Ask the pupil for the nearest whole, one decimal place and two decimal places without showing the completed examples. The first task is identifying which digit the instruction says to retain.

Nearest hundredth: the last retained place is hundredths and the deciding digit is the thousandths, 9. Since this digit is five or greater, the hundredths rounds upwards, with carrying when necessary. The answer to two decimal places is 5.00. This is an approximation of 4.999, not a claim that the original exact decimal has literally changed.

Nearest tenth: inspect the original hundredths digit, 9, immediately to the right of the tenths. It is five or greater, so the tenths rounds upwards. The answer to one decimal place is 5.0. Avoid simply rounding the previously written two-decimal answer again; use the given full original number and the requested place.

Nearest whole number: the deciding digit is the original tenths, 9. Because it is at least five, the nearest whole number is 5. The pupil can check that the original 4.999 lies close to the stated integer and that this instruction differs from reporting one or two decimal places.

Reasonableness check: the nearest-hundredth approximation 5.00 is exactly 1 thousandths away from 4.999, no greater than five thousandths under the ordinary positive-number convention. Ask how this would change if the thousandths digit were one lower or one higher, where that remains a valid digit. A new deciding digit provides more reliable evidence than copying these completed numerals.

30. Round 12.999 to three different accuracies

Independent task: a class number card contains 12.999, which has 12 as its whole-number part, 9 in the tenths place, 9 in the hundredths and 9 in the thousandths. Ask the pupil for the nearest whole, one decimal place and two decimal places without showing the completed examples. The first task is identifying which digit the instruction says to retain.

Nearest hundredth: the last retained place is hundredths and the deciding digit is the thousandths, 9. Since this digit is five or greater, the hundredths rounds upwards, with carrying when necessary. The answer to two decimal places is 13.00. This is an approximation of 12.999, not a claim that the original exact decimal has literally changed.

Nearest tenth: inspect the original hundredths digit, 9, immediately to the right of the tenths. It is five or greater, so the tenths rounds upwards. The answer to one decimal place is 13.0. Avoid simply rounding the previously written two-decimal answer again; use the given full original number and the requested place.

Nearest whole number: the deciding digit is the original tenths, 9. Because it is at least five, the nearest whole number is 13. The pupil can check that the original 12.999 lies close to the stated integer and that this instruction differs from reporting one or two decimal places.

Reasonableness check: the nearest-hundredth approximation 13.00 is exactly 1 thousandths away from 12.999, no greater than five thousandths under the ordinary positive-number convention. Ask how this would change if the thousandths digit were one lower or one higher, where that remains a valid digit. A new deciding digit provides more reliable evidence than copying these completed numerals.

31. Round 2.345 to three different accuracies

Independent task: a class number card contains 2.345, which has 2 as its whole-number part, 3 in the tenths place, 4 in the hundredths and 5 in the thousandths. Ask the pupil for the nearest whole, one decimal place and two decimal places without showing the completed examples. The first task is identifying which digit the instruction says to retain.

Nearest hundredth: the last retained place is hundredths and the deciding digit is the thousandths, 5. Since this digit is five or greater, the hundredths rounds upwards, with carrying when necessary. The answer to two decimal places is 2.35. This is an approximation of 2.345, not a claim that the original exact decimal has literally changed.

Nearest tenth: inspect the original hundredths digit, 4, immediately to the right of the tenths. It is below five, so the tenths stays at its existing value. The answer to one decimal place is 2.3. Avoid simply rounding the previously written two-decimal answer again; use the given full original number and the requested place.

Nearest whole number: the deciding digit is the original tenths, 3. Because it is below five, the nearest whole number is 2. The pupil can check that the original 2.345 lies close to the stated integer and that this instruction differs from reporting one or two decimal places.

Reasonableness check: the nearest-hundredth approximation 2.35 is exactly 5 thousandths away from 2.345, no greater than five thousandths under the ordinary positive-number convention. Ask how this would change if the thousandths digit were one lower or one higher, where that remains a valid digit. A new deciding digit provides more reliable evidence than copying these completed numerals.

32. Round 6.985 to three different accuracies

Independent task: a class number card contains 6.985, which has 6 as its whole-number part, 9 in the tenths place, 8 in the hundredths and 5 in the thousandths. Ask the pupil for the nearest whole, one decimal place and two decimal places without showing the completed examples. The first task is identifying which digit the instruction says to retain.

Nearest hundredth: the last retained place is hundredths and the deciding digit is the thousandths, 5. Since this digit is five or greater, the hundredths rounds upwards, with carrying when necessary. The answer to two decimal places is 6.99. This is an approximation of 6.985, not a claim that the original exact decimal has literally changed.

Nearest tenth: inspect the original hundredths digit, 8, immediately to the right of the tenths. It is five or greater, so the tenths rounds upwards. The answer to one decimal place is 7.0. Avoid simply rounding the previously written two-decimal answer again; use the given full original number and the requested place.

Nearest whole number: the deciding digit is the original tenths, 9. Because it is at least five, the nearest whole number is 7. The pupil can check that the original 6.985 lies close to the stated integer and that this instruction differs from reporting one or two decimal places.

Reasonableness check: the nearest-hundredth approximation 6.99 is exactly 5 thousandths away from 6.985, no greater than five thousandths under the ordinary positive-number convention. Ask how this would change if the thousandths digit were one lower or one higher, where that remains a valid digit. A new deciding digit provides more reliable evidence than copying these completed numerals.

33. Round 6.574 to three different accuracies

Independent task: a class number card contains 6.574, which has 6 as its whole-number part, 5 in the tenths place, 7 in the hundredths and 4 in the thousandths. Ask the pupil for the nearest whole, one decimal place and two decimal places without showing the completed examples. The first task is identifying which digit the instruction says to retain.

Nearest hundredth: the last retained place is hundredths and the deciding digit is the thousandths, 4. Since this digit is less than five, the hundredths remains unchanged. The answer to two decimal places is 6.57. This is an approximation of 6.574, not a claim that the original exact decimal has literally changed.

Nearest tenth: inspect the original hundredths digit, 7, immediately to the right of the tenths. It is five or greater, so the tenths rounds upwards. The answer to one decimal place is 6.6. Avoid simply rounding the previously written two-decimal answer again; use the given full original number and the requested place.

Nearest whole number: the deciding digit is the original tenths, 5. Because it is at least five, the nearest whole number is 7. The pupil can check that the original 6.574 lies close to the stated integer and that this instruction differs from reporting one or two decimal places.

Reasonableness check: the nearest-hundredth approximation 6.57 is exactly 4 thousandths away from 6.574, no greater than five thousandths under the ordinary positive-number convention. Ask how this would change if the thousandths digit were one lower or one higher, where that remains a valid digit. A new deciding digit provides more reliable evidence than copying these completed numerals.

34. Round 4.325 to three different accuracies

Independent task: a class number card contains 4.325, which has 4 as its whole-number part, 3 in the tenths place, 2 in the hundredths and 5 in the thousandths. Ask the pupil for the nearest whole, one decimal place and two decimal places without showing the completed examples. The first task is identifying which digit the instruction says to retain.

Nearest hundredth: the last retained place is hundredths and the deciding digit is the thousandths, 5. Since this digit is five or greater, the hundredths rounds upwards, with carrying when necessary. The answer to two decimal places is 4.33. This is an approximation of 4.325, not a claim that the original exact decimal has literally changed.

Nearest tenth: inspect the original hundredths digit, 2, immediately to the right of the tenths. It is below five, so the tenths stays at its existing value. The answer to one decimal place is 4.3. Avoid simply rounding the previously written two-decimal answer again; use the given full original number and the requested place.

Nearest whole number: the deciding digit is the original tenths, 3. Because it is below five, the nearest whole number is 4. The pupil can check that the original 4.325 lies close to the stated integer and that this instruction differs from reporting one or two decimal places.

Reasonableness check: the nearest-hundredth approximation 4.33 is exactly 5 thousandths away from 4.325, no greater than five thousandths under the ordinary positive-number convention. Ask how this would change if the thousandths digit were one lower or one higher, where that remains a valid digit. A new deciding digit provides more reliable evidence than copying these completed numerals.

Questions Tai Hwan Grove parents ask

What is 7.486 rounded to two decimal places?

7.49, because the thousandths digit six makes the retained hundredths digit eight round up.

What is 7.486 to one decimal place?

7.5, because the original hundredths digit eight raises the tenths from four to five.

Why does 7.486 round to seven as a whole number?

Its original tenths digit is four, below five, so the ones digit remains seven.

How is rounding different from dropping digits?

Rounding selects the nearest value at the requested precision; simply deleting digits can choose the more distant candidate.

What happens when the retained hundredths digit is nine?

A round-up may carry into tenths or even the whole-number part, as in 7.495 becoming 7.50 to two decimal places.

What should a 3-pax tutor check?

The target place, deciding digit, carrying and an independently explained new number after a delay.

Syllabus, location and a responsible parent consultation

The MOE Primary Mathematics syllabus, Primary 4 Decimals study guide and Mathematics learning hub connect this rounding topic with wider number sense. The number cards are original illustrative exercises, not actual physical measurements.

Tai Hwan Grove is a landed-residential street near Lorong Chuan. The neighbourhood reference confirms geographic context but not an eduKate teaching venue. The eduKate 3-pax small-group reference describes an existing centre near Sixth Avenue MRT; do not assume a new centre or class is available in Tai Hwan Grove.

For a parent–student consultation, bring an uncorrected decimal rounding attempt and the earliest helpful hint. Confirm actual fees, session placement and journey, then compare a weekday or weekend time that leaves enough attention and rest. A different independently rounded number after a delay should be part of any learning review. See the Tai Hwan Crescent Primary 4 guide for a different mathematical skill.