Parent guide · 5 min read
Multiplying decimals for kids: count the places in both numbers
Multiplying decimals trips children up because the rule sounds backwards. With addition, the points line up. With multiplication they do not, and the answer can even be smaller than the numbers you started with. This guide explains the rule so it makes sense rather than being a trick to memorise, and goes through the examples that cause most of the mistakes.
Try this tonight
4 things you can do at home
Estimate before calculating
Round each number to something friendly. 3.2 × 1.5 is about 3 × 1.5, so the answer should be a little under 5. An estimate like this catches a misplaced point straight away, long before the working is finished.
Cross out the points and multiply as whole numbers
Treat 3.2 × 1.5 as 32 × 15. Use whichever written method your child already knows for whole numbers, such as the grid or the column method. 32 × 15 = 480.
Count the places in both numbers
3.2 has one place after the point and 1.5 has one, so there are two in total. Write the count down beside the working, so it is not forgotten once the multiplying is done.
Put the point back and compare with the estimate
Starting from the right of 480, move the point in two places to get 4.80, which is 4.8. That matches the estimate of a little under 5. If the answer had come out as 48 or 0.48, the estimate would have flagged it.
Why counting the places works
A decimal is a whole number divided by a power of 10. 0.6 is 6 tenths and 0.4 is 4 tenths. Multiplying tenths by tenths gives hundredths, because a tenth of a tenth is a hundredth. So 6 tenths × 4 tenths is 24 hundredths, which is 0.24.
That is all the rule is doing. One place means tenths, two places means hundredths, and multiplying two decimals adds the places up. A child who sees the rule as "tenths times tenths make hundredths" has understood it, rather than memorised it.
A worked example: when the answer needs a zero
Take 0.07 × 0.3. Multiply 7 × 3 = 21. The numbers have two places and one place, three in total, so the answer needs three places: 0.021. There are only two digits in 21, so a zero is added at the front to fill the gap before the point is placed.
The usual error is writing 0.21 here, which is ten times too big. An estimate catches it: 0.07 is about 0.1 and 0.3 is about a third of 1, so the answer should be a few hundredths, not a couple of tenths.
A worked example: a trailing zero in the answer
Take 2.5 × 0.4. Multiply 25 × 4 = 100. There are two places in total, so 100 becomes 1.00, which is 1. The trailing zeros after the point can be dropped. A child who has understood this will not be puzzled at a "decimal" question with a whole-number answer: two and a half times four tenths is one whole.
It is worth showing that the answer can be checked another way: 2.5 × 0.4 is the same as 0.4 taken two and a half times, which is 0.4 + 0.4 + 0.2 = 1.
The belief that multiplying always makes numbers bigger
With whole numbers, multiplying makes things bigger, so children expect it always will. Multiplying by a number less than 1 breaks that: 8 × 0.5 = 4, because half of 8 is 4. The result is smaller than the number you started with.
Reading × as "of" helps: 0.5 of 8, or 0.6 of 0.4. It also makes it clear why 0.6 × 0.4 is smaller than both numbers. Say this out loud when it comes up, since a child who believes the old rule may "correct" a right answer into a wrong one.
Signs it’s time for outside help
When home help has done what it can
- Lines up the decimal points as if adding.
- Counts the places in only one of the numbers.
- Gets an answer ten or a hundred times too big or too small and does not notice.
- Believes that multiplying must always give a bigger number.
- Writes 0.21 for 0.07 × 0.3 because the zero is lost.
- Is fine with whole-number multiplying but stalls once a decimal appears.
Questions parents ask
FAQ
How do you multiply decimals?
Multiply the numbers as if they were whole numbers, ignoring the points. Then count the decimal places in both numbers together and give the answer that many places.
Do the decimal points need to line up when multiplying?
No. Lining up the points is for adding and subtracting. For multiplying, the points are dealt with at the end, by counting places.
What grade do children learn to multiply decimals?
In the US Common Core, multiplying decimals to hundredths is introduced in Grade 5 (ages 10–11). Other curricula, including the Australian Curriculum, cover it across the upper primary years.
Why is the answer smaller when I multiply by 0.5?
Multiplying by 0.5 means taking half of the number. Half of something is less than the whole, so the answer is smaller. The same is true for any multiplier between 0 and 1.
Further reading
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