Secondary 1 G3 Mathematics Tutor Bukit Timah | Fractions, Decimals and Percentages Made Clear

Did you know? One quarter, 0.25 and 25% are three ways of describing exactly the same quantity. A student may recognise all three separately but hesitate when a question suddenly switches from a fraction to a percentage. The difficulty is often not arithmetic; it is recognising that the mathematical amount has not changed.

For families looking for a Secondary 1 G3 Mathematics tutor in Bukit Timah, fluency between fractions, decimals and percentages is a useful foundation check. It supports ratio, discounts, graphs, estimation and algebra. Here is a conversational guide to converting correctly, spotting misleading shortcuts and checking whether a result makes sense.

Quick answer: how do the three forms connect?

• Fraction to decimal: divide the numerator by the denominator. For example, 3/4 = 3 ÷ 4 = 0.75.
• Decimal to percentage: multiply by 100 and attach %. Thus 0.75 = 75%.
• Percentage to fraction: write the percentage over 100 and simplify. Thus 75% = 75/100 = 3/4.
• Fraction directly to percentage: calculate the fraction of 100%. Thus 2/5 = (2 ÷ 5) × 100% = 40%.

These operations change the representation, not the numerical amount. Be careful: multiplying 0.75 by 100 gives the numerical value 75, but the new *unit* is percent. The statements 0.75 = 75 and 0.75 = 75% are not equivalent.

The conversion table worth understanding

Fraction	Decimal	Percentage
1/2	0.5	50%
1/4	0.25	25%
3/4	0.75	75%
1/5	0.2	20%
2/5	0.4	40%
1/8	0.125	12.5%
3/8	0.375	37.5%

Instead of memorising every row, practise explaining one. Why is 1/8 equal to 12.5%? Because 1 ÷ 8 = 0.125, and 0.125 × 100% = 12.5%. The remaining rows follow the same principles.

Worked example 1: convert a fraction with an easy denominator

Convert 7/20 into a percentage.

Make the denominator 100: multiply numerator and denominator by five. Thus 7/20 = 35/100 = 35%. The decimal is 0.35.

Check the scale: seven out of twenty is less than half; 35% is less than 50%, so the answer is plausible.

You could alternatively divide 7 by 20 and multiply by 100%, obtaining the same result. Choosing a convenient denominator can make mental work quicker.

Worked example 2: what about a fraction with thirds?

Convert 2/3 to a percentage.

Divide 2 by 3: the decimal is 0.6666…, with six repeating. Therefore the percentage is 66.666…%, or 66 2/3% exactly.

If the question requests one decimal place, round it to 66.7%. Do not assert that 0.67 is *exactly* two thirds. It is only a rounded approximation.

Why does this matter? A later calculation that repeatedly substitutes 0.67 for the exact fraction may accumulate rounding error. Keep 2/3 in exact form when possible.

Worked example 3: percent values can exceed 100

Convert 125% into a fraction and decimal.

125% = 125/100 = 5/4 = 1.25. That is one and one-quarter times the reference quantity.

A percentage greater than 100 is not necessarily wrong. If a second quantity is 50 and the first is 62.5, the first is 125% of the second.

However, 125% cannot describe an ordinary subgroup of one fully counted, nonoverlapping population. The interpretation depends on what is being compared.

Worked example 4: a small decimal is not a large percentage

Convert 0.006 to a percentage.

Multiply by 100%: 0.006 = 0.6%. In fraction form, 0.006 = 6/1000 = 3/500.

A common mistake is to write 6%, because the learner shifts the decimal only one position or drops zeros too quickly. The correct conversion is 0.006 × 100 = 0.6.

Use a quick check: 1% is 0.01. Since 0.006 is smaller than 0.01, the percentage must be less than 1%. The answer 0.6% passes that test.

Worked example 5: compare a fraction and a percentage

Which is larger: 7/8 or 85%?

Convert 7/8 to decimal 0.875, which is 87.5%. Hence 7/8 > 85%.

The comparison can also be made by changing 85% into 17/20, then finding a common denominator. Either route preserves the underlying quantity.

When signs are negative, the order needs more care. For example, −75% is greater than −7/8 because −0.75 is closer to zero than −0.875. Number-line reasoning is useful here.

Percentage of an amount: start with the whole

Find 12.5% of $80.

Recognise 12.5% as 1/8. One eighth of $80 is $10.

The decimal method gives 0.125 × 80 = 10 as well. The fraction is often faster mentally, while the decimal method generalises easily.

Now find 37.5% of $80. Since 37.5% = 3/8, the result is 3 × (80/8) = $30. You can verify using 0.375 × 80 = 30.

The most important question is what the 100% whole represents. In both examples, it is the given $80.

A percentage-point warning

Suppose a school’s *fictional* participation rate changes from 40% to 50%.

The difference is 10 percentage points. The relative percentage increase is 10/40 × 100% = 25%.

This is why being able to convert percentages does not automatically mean a learner knows how to compare two rates. Percentage points subtract percentage values; relative percentage change compares the difference with the original rate.

For a full worked discussion, see percentage change, discounts and reverse percentages.

Linking conversions to ratios

Suppose red:blue counters = 2:3. There are five equal parts in all. Red represents 2/5 of the total, or 0.4, or 40%.

But red is 2/3 *of the blue quantity*, about 66.7% of blue. Both descriptions can be correct because their denominators refer to different wholes.

Before converting, ask “Two out of what?” If the answer is “two out of five total parts,” use 2/5. If it is “two compared with three blue parts,” use 2/3.

The ratio, fractions and sharing guide explores this distinction in greater detail.

Why leading and trailing zeros matter

The decimal 0.25 equals 0.250 exactly as a numerical value. Both represent 25%.

But 0.025 represents 2.5%, not 25%. One extra leading zero after the decimal changes the number by a factor of ten.

Similarly, 2.5 is 250%, while 0.25 is 25%. The percent symbol alone does not tell us whether the original number was above or below one.

Ask students to place 0.025, 0.25 and 2.5 on a number line before converting. This encourages magnitude awareness, not just mechanical decimal shifting.

A six-step self-check routine

Read the requested final form, name the reference whole, make the conversion, keep an exact fraction when useful, estimate the result and confirm the percentage sign is present.

For any quantity between zero and one, its corresponding percentage lies between 0% and 100%. A value of 1.6 corresponds to 160%. A negative decimal corresponds to a negative percentage, such as −0.2 = −20%.

These checks work across unfamiliar examples because they concern the *meaning* of the forms.

Ten-question mini diagnostic

• A. Convert 3/5 to a decimal and percentage.
• B. Convert 7/20 to a percentage.
• C. Convert 0.08 to a percentage.
• D. Convert 0.006 to a percentage.
• E. Convert 12.5% to a simplified fraction.
• F. Convert 125% to a decimal and simplified fraction.
• G. Which is larger: 7/8 or 85%?
• H. Find 37.5% of 80.
• I. Convert 2/3 to a percentage to one decimal place.
• J. In a ratio red:blue = 2:3, what percentage of all counters is red?

Answers with a quick reason

A. 0.6 and 60%; three divided by five gives 0.6.

B. 35%; 7/20 = 35/100.

C. 8%; 0.08 × 100% = 8%.

D. 0.6%; it is less than 1%.

E. 1/8; 12.5/100 = 0.125.

F. 1.25 and 5/4.

G. 7/8, since it is 87.5%.

H. 30; 37.5% is 3/8 and 3/8 × 80 = 30.

I. 66.7%, rounded to one decimal place.

J. 40%, because red occupies two of the five total parts.

Ask which wrong answers are due to an incorrect *whole* and which are due to an incorrect decimal move. Those call for different corrections.

A practical ten-minute revision

Spend three minutes converting four familiar fractions mentally: 1/2, 1/4, 1/5 and 1/8. Next give two unfamiliar fractions and ask for decimal division. Then change directions and ask for percentages written as simplified fractions.

Finish with two contextual questions, including one whose denominator is *not* the combined total. This tests whether the child understands the reference quantity instead of memorising a conversion table.

Return to one changed problem later in the week without the example visible. Independent conversion and a sensible size check are signs the skill is becoming robust.

Choosing Secondary 1 G3 support in Bukit Timah

A useful tutor distinguishes weak fraction concepts, decimal-place errors and confusion about the percentage base. Extra worksheets alone cannot tell parents which of these needs attention.

The eduKateSG Secondary 1 Mathematics small-group tutorial reference explains close feedback and guided corrections in three-student tutorials near Sixth Avenue MRT. The Bukit Timah G3 Mathematics tuition overview adds location-specific programme context. Timetables and suitability should be confirmed directly.

The MOE G2 and G3 Mathematics syllabus includes ratios, rational numbers and conversion between percentages, fractions and decimals in the Secondary 1 G3 foundation.

Frequently asked questions

### Is 0.5 equal to 5%?

No. 0.5 is 50%, while 5% is 0.05.

### Is 0.333… rational?

Yes, when the 3 repeats indefinitely it equals 1/3. Its corresponding percentage is 33 1/3% exactly.

### Why write 12.5% as 1/8?

The fraction can make exact mental calculations easier, especially when finding a portion of an amount divisible by eight.

### Can percentages be negative?

Yes, for signed comparisons or changes when context allows it. But an ordinary share of a nonnegative whole is normally between 0% and 100%.

### Should I always use a calculator?

No. Familiar conversions are useful to know mentally, and a quick estimate can catch input mistakes. Use a calculator where appropriate while preserving understanding.

Continue learning

• Rational numbers, fractions and number lines
• Percentage change and reverse percentages
• Ratio, fractions and sharing quantities
• Significant figures and estimation

The next time you see 3/8, don’t ask which conversion rule to memorise. Ask what portion it represents and how else that same amount could be written.