Comparing and Ordering Decimals
0.7 or 0.35? Most children pick the wrong one, and they pick it for a reason that made perfect sense with whole numbers.
Why children get this wrong
With whole numbers, more digits means a bigger number. 350 beats 7 without thinking about it. Children spend years building that rule, and then decimals break it.
0.7 is bigger than 0.35. Not by a little either. It is twice as big.
The reason is that the digits after the point are not an ordinary number. They are amounts in named columns, and the columns get smaller as you move right.
Compare from the left
The rule
Start with the whole numbers. If they differ, you are already finished.
If they match, compare the tenths. Then the hundredths. Stop at the first column where they differ.
For 0.7 against 0.35, the whole numbers are both 0, so move to tenths. There it is 7 against 3, and 7 wins. Nothing after that matters, because no amount of hundredths can make up a whole tenth of a gap.
The zero padding trick
Decimals of different lengths feel harder to compare. Make them the same length by adding zeros to the right.
0.7 becomes 0.70. Now compare 0.70 with 0.35 and it is just 70 against 35.
Why adding zeros is safe
A zero on the RIGHT-hand end of a decimal changes nothing. 0.7 and 0.70 and 0.700 are all the same amount, the same way 7 tenths and 70 hundredths are the same amount. A zero anywhere else does change the number, so only ever pad the right-hand end.
Zooming in on the line
When two decimals are genuinely close, zoom in. Between 0.3 and 0.4 there are ten more steps, each one hundredth.
Worked examples
Different whole numbers
- Look at the whole numbers first: 2 against 3.
- They are different, so the comparison is already over.
- 3 is more than 2, so 3.05 is larger.
- The 9 in 2.9 is tempting, but nine tenths is still less than one whole.
Same start, different lengths
- Whole numbers match, both 0. Move on.
- Pad to the same length: 0.4 becomes 0.40.
- Now compare tenths: 4 against 3. That already decides it.
- Or read them as hundredths: 40 against 38.
Putting four in order
- Pad everything to two decimal places: 0.50, 0.45, 0.09, 0.54.
- Now they are all hundredths, so read them as 50, 45, 9 and 54.
- Order those: 9, then 45, then 50, then 54.
- Write the answers back in their original form.
Common mistakes
1. Longer means bigger
Picking 0.35 over 0.7 because it has more digits. This is the big one, and it is not carelessness. It is a rule that worked perfectly for years and now does not. Say it out loud: after the point, more digits means finer pieces, not more stuff.
2. Padding on the wrong side
Turning 0.4 into 0.04 to match the length of 0.38. Zeros go on the right-hand end only. Adding one on the left shifts every digit into a smaller column and divides the number by ten.
3. Carrying on after the decision is made
Comparing 3.05 and 2.9 and getting stuck on the 9. Once one column differs, stop. Later columns cannot overturn it, because a whole is always worth more than any number of tenths under ten.
Practice questions
Seven questions. One attempt each, and the explanation appears once the answer is in.
Check yourself
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For parents
Do not tell your child the longer-means-bigger rule is wrong. Tell them it is right for whole numbers and wrong after a point, and ask them why. Working out the reason themselves is what makes it stick, because the old rule is strong and simply being contradicted will not shift it.
What to learn next
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