Ross MackellUK-qualified primary teacher · 12 min read

What's 0.3 × 0.2? Lots of children say 0.6. Plenty of adults do too. The answer is 0.06, and the reason why is the key to multiplying any decimal with confidence.

Multiplying decimals looks like a brand new skill, but it isn't. If your child can already multiply whole numbers, they're about 90% of the way there. The only new part is knowing where the decimal point goes, and there's a simple rule for that.

I'm Ross, a UK-qualified primary teacher with over ten years in the classroom. In this guide I'll show you the method I teach, why it works, worked examples from the simple to the SATs-style, the mistakes I see most often, and practice questions with answers.

What your child needs first

Multiplying decimals sits on top of three skills. If one of them is wobbly, decimals will feel hard, and the fix is to go back to that skill rather than drill more decimals.

• Times tables. 0.7 × 8 is really 7 × 8 in disguise. If your child has to count up in sevens, every decimal question takes twice as long. See how to learn times tables fast.
• Short multiplication. Most SATs-style questions, like 3.46 × 7, need a written method. If carrying is shaky, start with short multiplication step by step.
• Decimal place value. Knowing that in 2.35 the 3 is worth 3 tenths and the 5 is worth 5 hundredths. If that's not secure, read what is place value first.

In the national curriculum, children multiply one-digit numbers with up to two decimal places by whole numbers in Year 6, using written methods. It's a regular on the KS2 arithmetic paper.

The method in three steps

This is the method I teach every child, and it works for every decimal multiplication they'll meet in primary school and beyond.

Notice the estimate comes first, not last. That's on purpose. Children who estimate first catch their own mistakes, because an answer of 94 or 0.94 for 2.35 × 4 is obviously wrong when you were expecting about 8.

Why the method works

You don't need to explain this to a seven-year-old, but older children (and parents) find the rule much easier to trust once they see why it works. It comes straight from multiplying and dividing by 10.

Take 0.6 × 7. Make 0.6 ten times bigger and it becomes 6. Now 6 × 7 = 42. But we made the question ten times too big, so the answer is ten times too big. Divide by 10 to fix it: 42 ÷ 10 = 4.2.

Taking the decimal point out of a number with one decimal place is the same as multiplying it by 10. Taking it out of a number with two decimal places is the same as multiplying by 100. Putting the places back undoes it. That's all the rule is. If dividing by 10 and 100 isn't automatic yet, multiplying and dividing by 10, 100 and 1000 is the place to start.

Decimals times whole numbers

This is what your child meets in primary school, and it's what the SATs arithmetic paper tests most.

Example 1: 0.6 × 7

1. Estimate: 0.6 is a bit more than a half, so the answer is a bit more than half of 7. About 4.
2. Take the point out: 6 × 7 = 42.
3. There's one decimal place in 0.6, so the answer has one: 4.2. That matches the estimate.

Example 2: 2.35 × 4

This one needs short multiplication. Your child writes it out as 235 × 4.

1. Estimate: 2.35 is close to 2.5, and 2.5 × 4 = 10. So the answer is a bit under 10.
2. Ones: 5 × 4 = 20. Write 0, carry the 2.
3. Tens: 3 × 4 = 12, plus the carried 2 is 14. Write 4, carry the 1.
4. Hundreds: 2 × 4 = 8, plus the carried 1 is 9. Write 9. So 235 × 4 = 940.
5. There are two decimal places in 2.35, so count two places in from the right: 9.40. That's the same as 9.4, and it's just under 10, as expected.

The zero at the end is a common trap. It's fine to drop it at the end (9.40 = 9.4), but your child must count the decimal places before dropping it. More on that in the mistakes section.

Example 3: 0.04 × 3

1. Estimate: 0.04 is tiny, so the answer will be tiny too.
2. Take the point out: 4 × 3 = 12.
3. There are two decimal places in 0.04, so the answer needs two digits after the point: 0.12.

If the answer of the whole number multiplication doesn't have enough digits, add zeros at the front. For 0.02 × 3, you get 6, which needs two decimal places, so it becomes 0.06.

Bigger multiplications

The method doesn't change when the numbers get bigger. Only the whole number method does.

Example 4: 1.4 × 23

1. Estimate: 1.5 × 20 = 30. So the answer is roughly 30.
2. Take the point out: 14 × 23. That's a job for long multiplication (or the grid method if your child is still building up to it). 14 × 3 = 42 and 14 × 20 = 280, so 14 × 23 = 322.
3. There's one decimal place in the question, so the answer has one: 32.2. Close to 30, so it makes sense.

Example 5: 3.46 × 7

1. Estimate: 3.5 × 7 = 24.5. So about 24.
2. Take the point out: 346 × 7. Ones: 6 × 7 = 42, write 2, carry 4. Tens: 4 × 7 = 28, plus 4 is 32, write 2, carry 3. Hundreds: 3 × 7 = 21, plus 3 is 24, write 24. So 346 × 7 = 2422.
3. Two decimal places in the question, so two in the answer: 24.22. Right next to the estimate.

This is a classic Year 6 arithmetic question. The calculation is no harder than 346 × 7. Getting the decimal point right is what earns the mark.

A decimal times a decimal

Multiplying two decimals together, like 0.3 × 0.2, goes a little beyond what the Year 6 curriculum asks for, and it usually becomes routine in secondary school. But it often turns up in 11+ papers and with confident Year 6 children, and the same rule works perfectly. Just count the decimal places in both numbers.

Example 6: 0.3 × 0.2

1. Take the points out: 3 × 2 = 6.
2. Count the decimal places: one in 0.3 and one in 0.2. That's two altogether.
3. So the answer needs two decimal places: 0.06.

It surprises children that the answer is smaller than both numbers. Here's how to make sense of it: 0.2 of something is a small part of it, so 0.3 × 0.2 means "a small part of 0.3". That's going to be tiny. In fractions, it's 310 × 210 = 6100, which is 0.06.

Example 7: 1.5 × 0.4

1. Estimate: 0.4 is a bit less than a half, so the answer is a bit less than half of 1.5. Roughly 0.6 or 0.7.
2. Take the points out: 15 × 4 = 60.
3. One decimal place in each number, so two altogether: 0.60, which is 0.6.

5 common mistakes and how to fix them

Mistake 1: Lining up the decimal points

When children add and subtract decimals, lining up the points is exactly right. So they do the same when multiplying, and it causes chaos with carrying and place value.

The fix: multiplying is different. Take the decimal points out completely, multiply the whole numbers, and only think about the point at the very end.

Mistake 2: 0.3 × 0.2 = 0.6

Your child counts the decimal places in only one of the numbers, or just copies the decimal point across.

The fix: count the decimal places in every number in the question and add them up. Say it out loud: "one place, plus one place, is two places".

Mistake 3: Dropping the zero too early

For 1.5 × 0.4, your child works out 15 × 4 = 60, drops the zero to get 6, then counts two places and writes 0.06. The right answer is 0.6.

The fix: place the decimal point first, then tidy up. 60 with two decimal places is 0.60, and only then does it become 0.6.

Mistake 4: 0.02 × 3 = 0.6

Your child gets 6 and puts the point in front of it, without noticing that 0.6 only has one decimal place.

The fix: count the digits after the point in the answer. If there aren't enough, add zeros in front. 0.06 has two digits after the point, so it's right.

Mistake 5: Skipping the estimate

Every mistake above would be caught by a quick estimate. A child who expects "about 8" won't write 94.0 or 0.94 for 2.35 × 4.

The fix: make the estimate a habit, every single time, until your child does it without being asked. It takes ten seconds and saves marks.

Practice questions

Same three steps I use for every skill: watch, copy, practise. Do the first one out loud yourself, then let your child have a go at a similar one before they try the rest on their own. Cover the last two columns and ask your child to fill in the gaps.

Bonus question: what is 0.6 × 0.3? (Answer: 6 × 3 = 18, and there are two decimal places altogether, so 0.18.)

Watch out for 3.6 × 5. 36 × 5 = 180, so the answer is 18.0, which is just 18. It's a nice check that your child is counting places before tidying up the zero.

Ten minutes, a few times a week, is plenty. Only move on when they're getting three in a row right.

Frequently asked questions

How do you multiply decimals?

Take the decimal points out and multiply as if the numbers were whole numbers. Then count the total number of decimal places in the question, and give the answer the same number of decimal places. For example, 1.2 × 3: 12 × 3 = 36, and there's one decimal place, so the answer is 3.6.

Do you line up the decimal points when multiplying?

No. You line up decimal points when adding and subtracting, but not when multiplying. Multiply the digits as whole numbers and place the decimal point at the end by counting decimal places.

How do you multiply a decimal by a whole number?

Ignore the decimal point, multiply, then put back the same number of decimal places as the decimal had. For 0.8 × 6, work out 8 × 6 = 48. There's one decimal place, so the answer is 4.8.

What year do children learn to multiply decimals?

In England, children multiply and divide by 10, 100 and 1000 in Year 5, then multiply one-digit numbers with up to two decimal places by whole numbers in Year 6. It appears regularly on the KS2 SATs arithmetic paper.

Why is the answer smaller when you multiply two decimals?

Multiplying by a number less than 1 means taking a part of something, so the answer gets smaller. 0.5 × 8 is half of 8, which is 4. In the same way, 0.3 × 0.2 is a small part of 0.3, which is 0.06.

Sources and further reading

• Department for Education, National curriculum in England: mathematics programmes of study (multiplication and division, and fractions including decimals, Years 5 and 6)
• Standards and Testing Agency, Key stage 2 mathematics test framework
• Ross Mackell, Teacher's Perspective on YouTube