Primary Maths Decimals: Compare the Value, Not the Number of Digits

A public family teaching question about decimals asks how to explain why a number with more decimal digits can be smaller. The discussion is international; the lesson below applies that mathematical issue to Singapore primary practice. No personal details about the learner are needed to understand the problem.

For a concrete local reference, Unity Primary's 2025 P4 parent booklet lists decimal place value, comparing and ordering decimals. It is a school booklet for that year, rather than a claim about every school's current teaching sequence. Use your child's assigned work to choose the appropriate difficulty.

Begin with a whole that stays the same size

Draw two equal squares. Divide each into ten equal strips. Shade six strips in one square. In the other, divide every strip into ten smaller parts and shade 58 of those hundredths. The first picture represents 0.6; the second represents 0.58. Six tenths cover more of the same whole than 58 hundredths.

The phrase “same whole” matters. Comparing a shaded part of a large rectangle with a shaded part of a tiny rectangle can hide the number relationship. Keep the outlines identical so that the drawing illustrates the quantities, rather than introducing a size puzzle.

Give the digits their units

Write 0.6 as six tenths, then as 60 hundredths. Write 0.58 as 58 hundredths. Now both quantities use the same unit, and 60 hundredths is greater than 58 hundredths. Therefore 0.6 > 0.58. This explains the comparison before introducing a written shortcut.

Next compare 0.47 with 0.5. Ask your child to rename five tenths as 50 hundredths. The answer is 0.47 < 0.5 because 47 hundredths is less than 50 hundredths. Avoid saying that the shorter number always wins: 0.63 is greater than 0.6, so that rule would immediately fail.

Explain what a trailing zero does

Writing 0.6 as 0.60 does not add an amount. It expresses the same six tenths using hundredths. A zero hundredths digit means that there are no extra hundredths beyond those six tenths. Compare this with 0.06, which represents six hundredths. Moving a digit to another place changes its value; appending a zero at the right of a decimal does not.

Use a small chart headed ones, tenths and hundredths. Put 0.6, 0.60 and 0.06 on separate rows with their decimal points aligned. Ask which entries represent the same quantity, then ask the child to show the answer on the squares. The chart and picture should tell the same story.

Turn the meaning into a reliable written method

Compare whole-number parts first. If they match, compare tenths, then hundredths, then thousandths if needed. Stop at the first place that differs. For 2.36 and 2.4, the whole-number parts match, but three tenths is less than four tenths. Later digits cannot reverse that comparison.

A number line gives a second check. Mark 0.4 and 0.5, and divide the interval into ten equal steps. Each step is one hundredth. Place 0.47 seven steps after 0.4. It must be to the left of 0.5. Ask the child to describe the location before choosing an inequality symbol.

Use a short practice set that reveals the reasoning

Try these original comparisons: 0.7 and 0.68; 0.32 and 0.320; 1.09 and 1.1; 0.405 and 0.45. The answers are 0.7 > 0.68, 0.32 = 0.320, 1.09 < 1.1 and 0.405 < 0.45. For the last pair, rename 0.45 as 0.450 and compare thousandths.

Ask for one explanation using place-value language, rather than four unexplained symbols. Then let the child invent a pair in which the longer decimal is smaller and another in which it is larger. This checks whether the method transfers beyond a familiar example.

For follow-up work, browse the Primary Maths collection and select a few decimal questions from an appropriate level. Keep comparison, rounding and calculation errors separate when reviewing them: they require different corrections.