Did you know that 1/3 is not equal to 0.3? The decimal 0.3 means three tenths, while one third has the recurring decimal form 0.333…. Writing 0.3 without a rounding instruction changes the value.
Use a quick check: multiply the proposed decimal by 3. Three lots of 0.3 make 0.9, not 1. By contrast, three lots of one third make exactly 1. This exposes the difference without asking the child to memorise a longer conversion table.
Ask the tutor whether the difficulty comes from place value, fraction meaning, calculator display or rounding instructions. Then practise one exact answer and one explicitly rounded answer so the child learns when each form is appropriate.
eduKateSG · Bukit Timah · Parent learning guide
Find your next learning step
- Separate tenths from thirds
- Prove the difference quickly
- Understand the recurring decimal
- Follow the answer instruction
- Check the idea on new fractions
Choose another question in the Primary to SEC series guide
SECTION 1 OF 5
Read each notation by its place value
The fraction 1/3 means one whole divided into three equal parts. The decimal 0.3 means three tenths, which is 3/10. These are different partitions of the whole.
A hundred-square can show 0.3 exactly as 30 shaded hundredths. One third cannot be represented by a finite number of hundredths without approximation, because equal thirds do not align exactly with hundredths.
Ask the child to say each value aloud before converting it. If both are described simply as “point three,” the missing link may be meaning rather than calculation.
SECTION 2 OF 5
Use multiplication as a reasonableness check
If one part is one third, three equal parts must rebuild one whole: 3 × 1/3 = 1. If the proposed decimal is 0.3, then 3 × 0.3 = 0.9. The gap is 0.1.
This check is especially useful when a calculator display has been copied too early or shortened without a stated degree of accuracy. It turns an abstract warning about recurring decimals into a value the student can test.
Keep the language precise: 0.3 is an approximation to one third only when the task permits rounding to one decimal place. It is not an exact equality.
SECTION 3 OF 5
See why the threes continue
Dividing 1 by 3 gives 0.333… because each new remainder produces another 3 in the next decimal place. The dots show that the pattern continues.
Original teaching illustration: sharing $1 equally among three people cannot be expressed exactly to the nearest cent. Thirty-three cents each accounts for 99 cents, leaving 1 cent. The money context has its own practical rounding decision; it does not change the exact mathematical fraction.
At a suitable level, the student can compare 0.3, 0.33 and 0.333. Each gets closer to one third, but a finite string of threes is still an approximation.
SECTION 4 OF 5
Choose an exact fraction or a rounded decimal
Keep 1/3 when an exact answer is required or when later calculation can preserve the fraction. Convert only when the problem, representation or assessment instruction calls for a decimal.
If the question specifies one decimal place, one third becomes 0.3; to two decimal places it becomes 0.33. If it specifies significant figures, use the correct rule for that question. Do not assume every calculator answer should be copied in full.
For PSLE or secondary work, use the student’s actual syllabus and examination-year instructions. The teaching point is stable: write an equality only when the values are equal, and mark an approximation according to the required convention.
SECTION 5 OF 5
Test whether the child can transfer the distinction
Ask whether 2/3 = 0.6. A student who repeats the earlier shortcut may say yes; the multiplication check shows that three lots of 0.6 make 1.8, whereas three lots of two thirds make 2.
Then compare a terminating case such as 3/4 = 0.75. This prevents the overcorrection that no fraction can equal a finite decimal.
Keep a small record of the fraction, the decimal written, the required accuracy and the child’s check. The pattern helps a tutor distinguish place-value confusion from a rounding or calculator-reading problem.
Contents · Previous · Discuss your next step
Bring one useful example to a consultation
Bring one exercise where a fraction was converted to a decimal and the original instruction. Ask whether the answer should remain exact, be rounded or be expressed another way, and how the child will check equivalence independently. Confirm suitable 3-pax arrangements directly.
Continue with the closest guide
- Bukit Timah Primary to SEC tuition-help series
- Why Does My Child Think a Bigger Denominator Means a Bigger Fraction?
- Why Does My Child Add the Denominators When Adding Fractions?
- Why Does My Child Add the Same Number to Make an Equivalent Fraction?
Sources and scope
The examples are original teaching illustrations. The routines are practical educational guidance, not measured student outcomes, grade promises or universal mastery thresholds. The teaching approach follows the diagnosis, clear explanation and independent-practice principles in the eduKateSG reference below. Current examination context was checked on 11 October 2026. Use the syllabus for the student’s actual subject, level, candidate type and examination year.