Decimals: The Four Slips, and a Two-Minute Check

9 September 2026 · by Larry

A child who can tell you instantly that 35 cents is less than 50 cents will sit down with a worksheet and write that 0.35 is bigger than 0.5.

Both of those are the same child on the same day, and neither answer is careless. In the shop she is thinking about money. On the page she is looking at 35 and 5 and doing what she has been trained to do for years: the number with more digits is bigger.

That is the whole difficulty with decimals in one sentence. They are not new arithmetic. They are place value pointing in an unfamiliar direction, and almost every decimal mistake is that one idea not yet settled.

Why decimals are harder than they look

Up to this point, every rule a child has learned about numbers has been reliable. More digits means bigger. Adding puts the numbers under each other and you start from the right. A zero at the end changes everything.

Decimals quietly break all three.

Now 0.5 is bigger than 0.35 even though 35 is bigger than 5. Now you line up by the decimal point rather than the right-hand edge. Now a zero at the end changes nothing at all, while a zero in the middle changes everything.

None of this is unfair — it is completely consistent once you see the place value. But a child who is applying the old rules is not being sloppy. She is being consistent with what she was taught last year, and telling her to be more careful will not help, because carefulness is not the problem. This is the same shape as what happens with fractions, when they suddenly stop making sense.

The four slips

1. Longer looks bigger

0.35 read as "thirty-five" and 0.5 read as "five", so 0.35 wins. This is the most common one and the most revealing, because it shows the digits after the point are being read as a whole number rather than as tenths and hundredths.

The same child will often get 0.7 against 0.68 wrong for the same reason, and will get 0.70 against 0.68 right — which is a useful thing to notice, because it tells you exactly where the understanding stops.

2. Lining up the edges instead of the point

When adding or subtracting, the old habit is to line the numbers up on the right. With whole numbers that works perfectly. With 12.5 + 3.75 it produces nonsense, because the 5 tenths ends up under the 5 hundredths.

What makes this hard to spot is that the answer looks plausible. It is a number, it is in the right region, and unless you check the working you would not know.

3. The zero that goes missing

3.05 gets written or read as 3.5. Point seven gets written as .7 with nothing in front. Both come from treating the decimal part as a separate little number rather than as places.

3.05 and 3.5 are genuinely far apart, and a child who slides between them is not making a copying error — she has not yet built the idea that the position of a digit is doing the work, not the digit itself.

4. Decimals that are not decimals

Money and time both look like decimals and behave differently. $1.50 is a decimal and works normally. But 1.5 hours is not one hour and five minutes, and 2.30 on a clock is not two and a third of an hour.

This trips up children who have been told, reasonably, that money is a good way to think about decimals. Money is a good way to think about decimals. Time is not, and it is worth saying so out loud once rather than letting her discover the exception in a test.

The two-minute check

You do not need a worksheet for this. Write four numbers on any piece of paper:

0.5    0.35    0.405    0.45
Which is the biggest? Which is the smallest?

Then, whatever she answers, ask the far more useful question: "How do you know?"

The answer to that is the whole diagnosis. "Because 45 is more than 405" tells you she is reading whole numbers. "Because it has more numbers after the point" tells you the same thing more clearly. "Because five tenths is a half and the others are less than a half" tells you she has it, and you can stop worrying.

A second question, if you want to be sure: write a number between 0.5 and 0.6. A child who thinks decimals are whole numbers in disguise will often say there isn't one.

What actually helps

Say the number properly, out loud. Not "nought point three five" but "three tenths and five hundredths", at least while it is being learned. The way we normally read decimals aloud is exactly the reading that causes the mistake — it names the digits and hides the places.

Even up the lengths. Compare 0.5 with 0.35 by writing 0.50 against 0.35. Fifty hundredths against thirty-five hundredths, and it becomes obvious. This is not a trick to get the right answer; it is the reason the right answer is right, and it is worth saying that so she does not file it away as another arbitrary rule.

Use money for two places, then step past it. Money makes hundredths concrete because she already knows a shop. But money stops at two places, so once tenths and hundredths are secure, move to a number line marked from 0 to 1 — that is what makes thousandths make sense, and it is where 0.405 stops being confusing.

Line up the points, and write the zeros in. For adding and subtracting, the rule is one sentence: the points go under each other, and every gap gets a zero. 12.50 + 3.75 rather than 12.5 + 3.75. Filling the gaps turns it back into a sum that looks like every other sum she can already do.

What does not help

More decimal sums. If the place value is not there, twenty more questions produce twenty more chances to practise the same wrong idea, and the frustration is real on both sides. This is the same trap as with so-called careless mistakes, most of which turn out to be one specific misunderstanding repeating.

Also worth resisting: correcting the answer without finding out how she got it. 0.35 and 0.5 are one question, and being told which is bigger teaches her that one comparison. Asking how she knows tells you whether the next hundred comparisons will be right.

If it goes deeper than decimals

Sometimes the trouble is not decimals at all. If a child is unsure what the 4 means in 3,426, then tenths and hundredths were never going to land, because they are the same idea continued past the point.

That is worth checking before spending weeks on decimals — ask what each digit is worth in a four-digit number, and if that is shaky, that is the thing to work on. Going back one step is faster than pushing forward through something built on it. Decimals sit alongside fractions and percentages in upper primary, and they lean on each other, which is part of what changes between P4 and P5.

The short version

• Decimals are not new arithmetic. They are place value continued past the point, and nearly every mistake is that one idea not yet settled.
• Four slips: longer looks bigger, lining up edges instead of points, the missing zero, and time pretending to be a decimal.
• Write 0.5, 0.35, 0.405, 0.45 and ask which is biggest — then ask how she knows. The second question is the one that tells you something.
• Say the places out loud, even up the lengths, use money then a number line, and fill the gaps with zeros.
• If four-digit place value is shaky, start there instead.