Comparing decimals like 0.09 and 0.1

Q: Why is my child learning to compare decimals this way?

Teachers ask children to think about how big each decimal is, often with grids, number lines, or coins, because the obvious shortcuts lead to mistakes. Treating 0.25 and 0.3 like the whole numbers 25 and 3 gives the wrong answer. Seeing 0.3 as 30 hundredths makes the comparison clear. Reasoning about size gives your child a method that works every time, not only on easy pairs.

Q: Is it helpful to add a zero, like writing 0.3 as 0.30?

Yes, as long as your child understands why. Writing 0.3 as 0.30 does not change its value, because 3 tenths equals 30 hundredths. It makes both decimals use hundredths, so 0.30 and 0.25 can be compared directly. If your child can explain that the zero means there are no extra hundredths, it is a sound strategy rather than a trick.

Q: How can I tell if my child really understands decimal size?

Ask for an explanation, not only an answer. For example, "Which is more, 0.6 or 0.58, and how do you know?" A child who understands might say that 0.6 is 60 hundredths, which is more than 58 hundredths, or that 0.6 is like 6 dimes. Asking them to place both numbers on a number line between 0 and 1 is another good check.

In 4th grade, children learn to compare decimals to hundredths, like 0.09 and 0.1, by their size rather than how many digits they have; and to record the result with >, =, or <.

By Robert “Bobby” BarnettMath teacher, parent, and founder of Bobby’s Math Club

Try these with your child

These are real questions from our 4th grade practice. Tap the speaker to hear one read aloud, or the light bulb for a hint, and talk about the answer together.

Question 1 of 3

Mina's ribbon is 0.8 m long. Jae's ribbon is 0.80 m long. Which sign makes this true? 0.8 ___ 0.80

Why this matters

Learning to compare decimals by size, not length, protects your child from a mistake that can linger for years: thinking 0.25 is bigger than 0.3 because it has more digits. It matters in real life, from comparing prices to reading race times. In 5th grade they compare decimals to the thousandths and round them, and in middle school the same sense of size carries into percents.

Where kids can get stuck

Thinking a decimal with more digits is bigger, so 0.25 seems greater than 0.3, as if comparing 25 and 3.
Swinging to the opposite rule, that the shorter decimal always wins, and then saying 0.4 is greater than 0.45.
Assuming 0.5 of a small pizza is more than 0.3 of a large one, forgetting the wholes are different sizes.

How you can help

Compare prices under a dollar at the store, such as $0.89 and $0.95. Ask your child which costs more, then which is more money, 1 dime or 9 pennies, and write both as decimals.
Draw a number line from 0 to 1 on paper, marked in tenths. Have your child place 0.3, 0.25 and 0.7 on it and read off which is largest.
Look at rainfall totals in the weather report for two days, such as 0.4 and 0.35 inches. Have your child write the comparison with >, =, or <, then explain it using tenths and hundredths.

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Questions parents ask

Why is my child learning to compare decimals this way?

Teachers ask children to think about how big each decimal is, often with grids, number lines, or coins, because the obvious shortcuts lead to mistakes. Treating 0.25 and 0.3 like the whole numbers 25 and 3 gives the wrong answer. Seeing 0.3 as 30 hundredths makes the comparison clear. Reasoning about size gives your child a method that works every time, not only on easy pairs.

Is it helpful to add a zero, like writing 0.3 as 0.30?

Yes, as long as your child understands why. Writing 0.3 as 0.30 does not change its value, because 3 tenths equals 30 hundredths. It makes both decimals use hundredths, so 0.30 and 0.25 can be compared directly. If your child can explain that the zero means there are no extra hundredths, it is a sound strategy rather than a trick.

How can I tell if my child really understands decimal size?

Ask for an explanation, not only an answer. For example, "Which is more, 0.6 or 0.58, and how do you know?" A child who understands might say that 0.6 is 60 hundredths, which is more than 58 hundredths, or that 0.6 is like 6 dimes. Asking them to place both numbers on a number line between 0 and 1 is another good check.

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Written by Robert “Bobby” Barnett

Bobby is an award-winning math teacher, the author of Meet Every Learner’s Needs, and the father of two elementary-school math learners. He uses Bobby’s Math Club with his own kids a few times every week. Learn more or contact Bobby.

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Note for teachers: This skill is covered by Common Core math standard 4.NF.C.7: “Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.” Learn how Bobby's Math Club can help your students grow. (Common Core 4.NF.7)

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