Is 0.5 the same as 0.50?

Yes, exactly the same amount. The trailing zero says there are no hundredths, which changes nothing about the size, the way writing 50 cents as 0.50 dollars does not add money. Children find this easier to accept once they have seen both written under the same place value headings.

Why is my child fine with whole numbers but lost with decimals?

Because the rules they trust quietly reverse. With whole numbers the longer number is bigger and the last digit is the smallest unit, and after the decimal point neither of those holds. Decimals are not harder arithmetic, they are the same arithmetic with an assumption removed, which is why the confident children are sometimes the most tripped up.

When are decimals taught?

Tenths and hundredths appear in fourth grade, usually right after fractions, and comparing, ordering and calculating with them fills fifth. Comparing is the gateway skill: a child who cannot say which of two decimals is larger has no way to sense check an answer to a decimal sum later on.

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Bigger Decimal

Which decimal is larger?

Grades 4-5 · Comparing decimals by place value

How to play

1Two decimals appear.
2Tap the larger one.
3Compare place by place from the left. More digits does not mean bigger.
4Build a streak of correct comparisons.

Try a few

Which is larger, 0.45 or 0.5?
Answer: 0.5
Compare the first column after the point and stop as soon as it decides. 0.45 has 4 tenths, 0.5 has 5 tenths, and 5 tenths is more, so 0.5 wins before the 5 in the hundredths column gets a vote at all. The hundredths only matter when the tenths tie. In money that is 45 cents against 50 cents, and no child has ever thought 45 cents was the bigger pile.
Which is larger, 0.7 or 0.09?
Answer: 0.7
This is the pair that catches children who read 9 against 7 and answer 0.09. Look at the tenths column instead: 0.7 has 7 tenths, 0.09 has none, because its 9 sits one column further right in the hundredths. Writing the short one as 0.09 and the long one as 0.70 lines the columns up and the gap becomes obvious, 70 hundredths against 9.
Which is larger, 1.6 or 1.53?
Answer: 1.6
The whole numbers match, so they settle nothing and the comparison moves right. Tenths next: 6 against 5, and 6 wins, so 1.6 is larger and the 3 in 1.53 never gets considered. When the whole numbers differ, as in 2.05 against 1.99, the job is already finished on the left and nothing after the point needs reading. Always start at the left and stop at the first column that differs.

Why this game helps

The classic decimal error is treating what follows the point as a whole number, so 0.45 is judged bigger than 0.5 on the grounds that forty-five beats five. It is a reasonable reading and it is wrong, because those digits are tenths and hundredths, not units, and four tenths is less than five tenths whatever comes after. Lining the numbers up by place value, rather than by length, is the whole skill. Money is the useful anchor for most children, since nobody thinks 45 cents is more than 50 cents.

If your child finds this hard

The error to expect is more digits means bigger, so 0.45 gets chosen over 0.5 and 0.38 over 0.4. The reasoning is sound for whole numbers, where a longer number really is larger, and the child is carrying a rule that has quietly stopped applying. Say plainly that after the point the length means how finely the number is cut, not how much there is, and that 0.5 and 0.50 are the same amount written two ways.

The related slip is comparing the digits after the point as if they were a whole number, which is what makes a child call 0.09 bigger than 0.7 on the grounds that nine beats seven. Pad the shorter one with a zero so both have the same number of places, 0.70 against 0.09, and then the digits can be read as 70 and 9 without lying about the place value. Padding is a crutch, but it is a crutch that tells the truth.

If both of those keep recurring, put money on the table and stop talking about decimals for a session. A dollar cut into ten dimes and a hundred pennies is the tenths and hundredths columns in a form a child already trusts, and 0.45 becomes four dimes and five pennies. Then move to a place value chart with the columns drawn and the point fixed in one spot, so comparing means reading down the columns rather than scanning along the digits.

Common questions

Is 0.5 the same as 0.50?: Yes, exactly the same amount. The trailing zero says there are no hundredths, which changes nothing about the size, the way writing 50 cents as 0.50 dollars does not add money. Children find this easier to accept once they have seen both written under the same place value headings.
Why is my child fine with whole numbers but lost with decimals?: Because the rules they trust quietly reverse. With whole numbers the longer number is bigger and the last digit is the smallest unit, and after the decimal point neither of those holds. Decimals are not harder arithmetic, they are the same arithmetic with an assumption removed, which is why the confident children are sometimes the most tripped up.
When are decimals taught?: Tenths and hundredths appear in fourth grade, usually right after fractions, and comparing, ordering and calculating with them fills fifth. Comparing is the gateway skill: a child who cannot say which of two decimals is larger has no way to sense check an answer to a decimal sum later on.

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