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

How do you divide decimals?

To divide a decimal by a whole number, divide the digits as usual and keep the decimal point in the same place. It helps to think in tenths or hundredths. 2.4 is 24 tenths, and 24 tenths ÷ 6 is 4 tenths, so 2.4 ÷ 6 = 0.4.

There are three steps:

1. Estimate. Round the decimal and divide in your head.
2. Divide. Use a division fact, short division or long division.
3. Place the point. The point in the answer goes directly above the point in the number being divided. Check against the estimate.

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

Dividing decimals by 10, 100 and 1,000

When you divide by 10, the number becomes a tenth of the size, so every digit moves one place to the right on a place value chart. Dividing by 100 moves each digit two places, and by 1,000 three places. The decimal point stays where it is, between the ones and the tenths.

45.6 in a place value chart

Tens	Ones	Tenths
4	5	6

45.6 ÷ 10 = 4.56: the 4 tens become 4 ones, the 5 ones become 5 tenths and the 6 tenths become 6 hundredths. In the same way, 7 ÷ 100 = 0.07, and 350 ÷ 1,000 = 0.35. A zero goes in the ones place when nothing else is there, so the answer is written 0.07 and not .07. There's more on this in our guide to place value.

Children divide whole numbers and decimals by 10, 100 and 1,000 in Year 5. In Year 6 the answers can have three decimal places, such as 6.5 ÷ 100 = 0.065.

Using division facts with decimals

Every division fact from the times tables gives a family of decimal facts. Government guidance for teachers gives examples like this: 15 ÷ 3 = 5, so 0.15 ÷ 3 = 0.05. Children say "15 hundredths divided by 3 is 5 hundredths." In the same way, 0.12 ÷ 4 = 0.03, and 5.6 ÷ 7 = 0.8, because 56 tenths divided by 7 is 8 tenths.

Division facts come straight from the times tables, so a child who knows 7 × 8 = 56 already knows 5.6 ÷ 7 = 0.8.

How do we divide decimals by whole numbers?

To divide a decimal by a whole number, set it out as short division (the bus stop method), divide each digit from the left, and write the decimal point in the answer above the point underneath. For a two-digit whole number, use long division in the same way.

Worked example: 7.35 ÷ 5

Estimate first: 7.35 is about 7.5, and 7.5 ÷ 5 = 1.5. The working is the same as 735 ÷ 5:

1. How many 5s in 7? 1, because 1 × 5 = 5, with 2 left over. Write 1 above and carry the 2 to the next digit.
2. The 2 hundreds carried make 23 tens. How many 5s in 23? 4, because 4 × 5 = 20, with 3 left over. Write 4 above and carry the 3 to the next digit.
3. The 3 tens carried make 35 ones. 35 ÷ 5 = 7. Write 7 above.

7.35 is 735 hundredths, and 735 hundredths ÷ 5 is 147 hundredths. So 7.35 ÷ 5 = 1.47. When children write 7.35 under the bus stop, they put the point in the answer above the point in 7.35, straight after the 1. The answer is close to the estimate.

Worked example: £8.52 shared between 3

Money is where children meet this most. £8.52 is 852 pence, so share 852 between 3:

1. How many 3s in 8? 2, because 2 × 3 = 6, with 2 left over. Write 2 above and carry the 2 to the next digit.
2. The 2 hundreds carried make 25 tens. How many 3s in 25? 8, because 8 × 3 = 24, with 1 left over. Write 8 above and carry the 1 to the next digit.
3. The 1 ten carried makes 12 ones. 12 ÷ 3 = 4. Write 4 above.

That's 284 pence each, which is £2.84. As a decimal sum, 8.52 ÷ 3 = 2.84. Check with the inverse: £2.84 × 3 should give back £8.52.

Division with decimals in the answer

When a whole number doesn't divide exactly, the answer can be written as a decimal instead of a remainder. The national curriculum gives the example 98 ÷ 4 = 24.5: four 24s are 96, and the 2 left over is half of 4, which is 0.5.

In a written method, write a decimal point and zeros after the number, then keep dividing. For 9 ÷ 4, write 9 as 9.00. That's 900 hundredths:

1. How many 4s in 9? 2, because 2 × 4 = 8, with 1 left over. Write 2 above and carry the 1 to the next digit.
2. The 1 hundred carried makes 10 tens. How many 4s in 10? 2, because 2 × 4 = 8, with 2 left over. Write 2 above and carry the 2 to the next digit.
3. The 2 tens carried make 20 ones. 20 ÷ 4 = 5. Write 5 above.

900 hundredths ÷ 4 is 225 hundredths, so 9 ÷ 4 = 2.25. In the bus stop, the 1 left over after 9 ÷ 4 is carried onto the first zero to make 10 tenths, and so on. In Year 6, children use written division where the answer has up to two decimal places, like this one. For fractions like a third, which never divide exactly, see fractions to decimals and rounding.

Which year do children learn to divide decimals?

Children divide decimals by 10, 100 and 1,000 in Year 5, and divide decimals by whole numbers in Year 6:

• Year 5: divide whole numbers and decimals by 10, 100 and 1,000, and write some division answers as decimals.
• Year 6: divide by 10, 100 and 1,000 with answers up to three decimal places. Use written division where the answer has up to two decimal places, dividing by one-digit and two-digit whole numbers, often in money and measures. Estimate to check the answer is sensible.

Dividing by a decimal, like 4.8 ÷ 0.6, comes at secondary school (see below). See the Year 5 maths and Year 6 maths guides for the rest of these years, and multiplying decimals for the inverse.

Common mistakes when dividing decimals

• Forgetting a zero in the answer. 6.24 ÷ 6 = 1.04. Writing 1.4 misses the 0 tenths: 6 doesn't go into 2 tenths, so a 0 must go above the 2.
• The point in the wrong place. If the points aren't lined up, 7.35 ÷ 5 can come out as 14.7. An estimate shows straight away that it must be about 1.5.
• "Take off a zero." That works for 450 ÷ 10, but 4.5 ÷ 10 is 0.45, not 4.5 or 0.5. Think "a tenth of the size" instead.
• Stopping at a remainder. With money or measures, 9 ÷ 4 needs 2.25, not "2 remainder 1".
• Missing the zero before the point. Write 0.07, not .07.

How to help at home

• Split a bill. "£7.20 between 4 of us: how much each?" Money makes the decimal point feel real.
• Use measures. "Cut this 1.5 metre ribbon into 3 equal pieces. How long is each one?"
• Estimate first, check after. Ask for a rough answer before the working, then check by multiplying back.
• Keep the division facts fresh. The times table check practice and the times table grid both help.

At secondary school: how to divide decimals by a decimal

Dividing by a decimal comes in Key Stage 3, where children use the four operations with decimals. The trick is to make the number you're dividing by a whole number first. Multiply both numbers by 10 (or 100), and the answer doesn't change.

For 4.8 ÷ 0.6, multiply both by 10. 48 ÷ 6 = 8, so 4.8 ÷ 0.6 = 8 too. For 1.5 ÷ 0.03, multiply both by 100: 150 ÷ 3 = 50, so 1.5 ÷ 0.03 = 50.

The answer is bigger than the number you started with, which surprises many children. That's because you're asking how many 0.6s fit into 4.8, and small pieces fit in many times.

Dividing decimals questions to try

1. 56.4 ÷ 10
2. 3.8 ÷ 100
3. 0.24 ÷ 6
4. 8.46 ÷ 3
5. 7 ÷ 4, as a decimal
6. 5.16 ÷ 12

Answers

1. 5.64
2. 0.038
3. 0.04 (24 hundredths ÷ 6 is 4 hundredths)
4. 2.82 (846 ÷ 3 = 282 hundredths)
5. 1.75 (write 7 as 7.00)
6. 0.43 (516 ÷ 12 = 43 hundredths; 12 doesn't go into 5, so the answer starts 0.)

For everything else in Key Stage 2, see the KS2 maths hub, or the decimals guide for the place value behind all of this.