Multiplying decimals: a step-by-step guide for parents

How do you multiply decimals?

To multiply decimals, multiply the digits as whole numbers, then make the answer the right size again. The easiest way to see why this works is to count in tenths or hundredths. 0.7 is 7 tenths, so 0.7 × 6 is 42 tenths, and 42 tenths is 4.2. So 0.7 × 6 = 4.2.

There are three steps:

1. Estimate. Round the decimal to a whole number and multiply in your head.
2. Multiply without the point. Use a times tables fact, short multiplication or long multiplication on the digits.
3. Put the point back. If the decimal had one decimal place, the answer has one decimal place too. Then check it against the estimate.

The rest of this page goes through each kind of decimal multiplication in the order children meet it at school.

Multiplying decimals by 10, 100 and 1,000

When you multiply by 10, the number becomes 10 times the size, so every digit moves one place to the left on a place value chart. Multiplying by 100 moves each digit two places, and by 1,000 three places. The decimal point itself stays put, between the ones and the tenths.

3.45 in a place value chart

Ones	Tenths	Hundredths
3	4	5

3.45 × 10 = 34.5: the 3 ones become 3 tens, the 4 tenths become 4 ones and the 5 hundredths become 5 tenths. In the same way, 3.45 × 100 = 345 and 0.6 × 1,000 = 600. If there are empty places at the end, fill them with zeros, which is why 0.6 becomes 600. There's more on this in our guide to place value.

Children multiply decimals by 10, 100 and 1,000 in Year 5. In Year 6 they do the same with numbers given to three decimal places, such as 2.375 × 100 = 237.5.

Using times tables facts with decimals

A times tables fact gives a whole family of decimal facts. Government guidance for teachers calls this scaling: if 3 × 5 = 15, then 3 × 0.5 = 1.5 and 3 × 0.05 = 0.15. Children say it in place value words: "3 times 5 hundredths is 15 hundredths, and 15 hundredths is 0.15."

The national curriculum starts with the simplest cases, such as 0.4 × 2 = 0.8. From there children move on to facts that cross a whole number, like 0.8 × 7 = 5.6 (8 tenths × 7 is 56 tenths). Secure times tables make all of this much easier, especially the 7s and 8s.

How do you multiply a whole number by a decimal?

To multiply a whole number by a decimal, multiply as if the decimal were a whole number, then divide the answer by 10 or 100 to put the point back. Use short multiplication for a one-digit whole number and long multiplication for a two-digit one. The order doesn't matter: 6 × 3.47 is the same as 3.47 × 6.

Worked example: 3.47 × 6

Estimate first: 3.47 is about 3.5, and 3.5 × 6 = 21. Then work out 347 × 6, ignoring the point for now.

1. Ones: 7 × 6 = 42. Write 2 in the ones column and carry 4 into the tens column.
2. Tens: 4 × 6 = 24, plus the 4 carried makes 28. Write 8 in the tens column and carry 2 into the hundreds column.
3. Hundreds: 3 × 6 = 18, plus the 2 carried makes 20. Write 20.

3.47 is 347 hundredths, so 3.47 × 6 is 2,082 hundredths. 2,082 hundredths is 20.82, so 3.47 × 6 = 20.82. That's close to the estimate of 21, so the point is in the right place.

At school, children often write the decimal straight into the short multiplication, with the point in its own column. The digits are multiplied in exactly the same way as above, and the point in the answer goes directly below the point in 3.47.

Worked example: £2.65 × 14

The curriculum asks children to multiply decimals by two-digit whole numbers too, often with money. Say a ticket costs £2.65 and 14 people go. Estimate: about £3 × 14, which is £42. Then work out 265 × 14.

1. Multiply by the 4 ones: 265 × 4 = 1,060.
2. Multiply by the 1 ten, which is × 10: write a 0 in the ones column first as a placeholder, then 265 × 1 = 265, so 265 × 10 = 2,650.
3. Add the rows: 1,060 + 2,650 = 3,710.

£2.65 is 265 pence, so the total is 3,710 pence, or £37.10. As a decimal sum, 2.65 × 14 = 37.1. With money we write the zero on the end, because prices always show two decimal places. The answer is a bit under the estimate of £42, which makes sense, because £2.65 is less than £3.

Which year do children learn to multiply decimals?

Children start multiplying decimals in Year 5, and multiply decimals by whole numbers in Year 6:

• Year 5: multiply whole numbers and decimals by 10, 100 and 1,000. Teachers also use scaled times tables facts like 3 × 0.05 = 0.15.
• Year 6: multiply and divide by 10, 100 and 1,000 with answers up to three decimal places. Multiply one-digit numbers with up to two decimal places, like 3.47, by whole numbers, often in money and measures. Use estimating and rounding to check answers.

Multiplying two decimals together, like 0.3 × 0.2, isn't part of the primary curriculum. It comes at secondary school (see below). For the rest of these years, see the Year 5 maths and Year 6 maths guides. Dividing works the same way in reverse: see dividing decimals.

Common mistakes when multiplying decimals

• The point in the wrong place. 3.47 × 6 written as 208.2 or 2.082. An estimate catches this every time: the answer has to be about 21.
• "Just add a zero." That works for 23 × 10, but 3.4 × 10 isn't 3.40. It's 34. Think "10 times the size" instead.
• Lining up the digits on the right. When a decimal is written in a column method, the decimal points must line up, not the last digits.
• Dropping the money zero. £37.1 should be written £37.10, even though 37.1 and 37.10 are the same number.
• A times tables slip. Most wrong answers come from a fact, not the decimal point. The times table grid is handy for checking.

How to help at home

• Use money. "Three drinks at £1.45 each: about how much?" Then work it out exactly. Money is the context schools use most.
• Use measures. "Each shelf is 0.8 metres. How long are 5 shelves end to end?"
• Estimate out loud. Before any decimal calculation, ask "about how big will the answer be?"
• Say it in tenths. "6 tenths times 4 is 24 tenths, which is 2.4." This builds the habit that makes the decimal point make sense.

At secondary school: decimals times decimals

Multiplying a decimal by a decimal comes in Key Stage 3, where children use the four operations, including the written methods, with decimals. The method is the same: multiply the digits as whole numbers, then count the decimal places in both numbers together. That's how many the answer needs.

For 1.2 × 0.4: 12 × 4 = 48, and there are two decimal places in the question (one in each number), so 1.2 × 0.4 = 0.48. In the same way, 0.3 × 0.2 = 0.06.

The surprise for many children is that multiplying by a decimal less than 1 makes a number smaller. 2.5 × 0.4 = 1, which is less than 2.5, because you're finding 4 tenths of 2.5.

Multiplying decimals questions to try

1. 0.6 × 4
2. 4.7 × 10, then 0.08 × 100
3. 1.25 × 3
4. 4.36 × 7
5. £3.45 × 12
6. 0.06 × 5

Answers

1. 2.4 (6 tenths × 4 is 24 tenths)
2. 47, then 8
3. 3.75
4. 30.52 (436 × 7 = 3,052, so 3,052 hundredths; estimate 4 × 7 = 28)
5. £41.40 (345 × 12 = 4,140 pence)
6. 0.3 (6 hundredths × 5 is 30 hundredths, which is 3 tenths)

For everything else in Key Stage 2, see the KS2 maths hub, or start with decimals if the place value side needs a refresh.