Rounding numbers: the rule, the 5 question and decimals

What does rounding mean?

Rounding is a way of making a number simpler while keeping it close to the real value. A crowd of 4,872 people is "about 5,000". A price of £2.95 is "about £3". Government guidance for teachers puts it plainly: numbers are rounded to get rid of detail you don't need, and rounded numbers give estimates.

Rounding always has a target: the nearest 10, the nearest 100, the nearest whole number, one decimal place and so on. The same number rounds differently to different targets, so the question always says which one.

How to round numbers

To round a number, find the two numbers either side of it that you could round to, then choose the one it's nearer to. Schools teach this in two steps:

1. Find the multiples either side. 347 is between 340 and 350 (the previous and next multiples of 10).
2. Pick the nearer one. 347 is 7 away from 340 and 3 away from 350, so it rounds to 350.

The shortcut is to look at the digit just to the right of the place you're rounding to. Rounding to the nearest 10, look at the ones digit. If it's 5 or more, round up. If it's 4 or less, round down. In 347 the ones digit is 7, so round up to 350.

Children start with a number line, like the one above, and by the end of Year 4 they're expected to round without one.

Rounding to the nearest 10

Rounding to the nearest 10 means finding the nearest number that ends in 0. Look at the ones digit:

• 63 rounds to 60 (3 is less than 5, so round down)
• 68 rounds to 70 (8 is 5 or more, so round up)
• 681 rounds to 680
• 2,396 rounds to 2,400, because the next multiple of 10 after 2,390 is 2,400

The groundwork starts well before Year 4. In Year 2, children learn which two multiples of 10 a number like 47 sits between, and in Year 3 they do the same with multiples of 10 and 100 for numbers like 681.

Rounding to the nearest 100 and 1,000

The method is the same: look at the digit to the right of the place you're rounding to. To round to the nearest 100, look at the tens digit. To round to the nearest 1,000, look at the hundreds digit.

Worked example: round 8,681 to the nearest 100 and to the nearest 1,000.

• Nearest 100: 8,681 is between 8,600 and 8,700. The tens digit is 8, so round up to 8,700.
• Nearest 1,000: 8,681 is between 8,000 and 9,000. The hundreds digit is 6, so round up to 9,000.

In Year 5 this stretches to numbers up to 1,000,000, rounded to the nearest 10,000 or 100,000 as well. 346,512 to the nearest 10,000 is 350,000, because the thousands digit is 6.

What happens with a 5?

A number exactly halfway rounds up. 45 is halfway between 40 and 50, so 45 rounded to the nearest 10 is 50. In the same way, 250 rounded to the nearest 100 is 300, and 4.5 rounded to the nearest whole number is 5.

This is a convention, the rule everyone agrees to use, rather than because 45 is any closer to 50. With the "5 or more, round up" shortcut, children don't need to think about halfway at all.

One trap: only the digit straight after the rounding place matters. 3,449 to the nearest 1,000 is 3,000, because the hundreds digit is 4. It doesn't "round up in a chain" from the 9.

Rounding decimals to the nearest whole number

To round a decimal to the nearest whole number, look at the tenths digit, the first digit after the decimal point. Children do this with one decimal place in Year 4 and two decimal places in Year 5.

• 3.7 rounds to 4 (7 tenths is 5 or more)
• 12.3 rounds to 12
• 8.61 rounds to 9 (look only at the 6)

There's more on tenths and hundredths in our guide to decimals.

How do you round to 1 decimal place?

To round to 1 decimal place (the nearest tenth), look at the hundredths digit, the second digit after the point. This comes in Year 5.

Worked example: round 8.61 and 3.47 to 1 decimal place.

1. 8.61 is between 8.6 and 8.7. The hundredths digit is 1, so round down: 8.6.
2. 3.47 is between 3.4 and 3.5. The hundredths digit is 7, so round up: 3.5.

Watch out for 9s. 2.96 to 1 decimal place is 3.0, because 2.9 goes up to 3.0. Keep the zero: it shows the answer is to 1 decimal place.

How to round to 2 decimal places

To round to 2 decimal places (the nearest hundredth), look at the third digit after the point. 2.346 is between 2.34 and 2.35, and the thousandths digit is 6, so it rounds to 2.35. Money works this way: an answer of £4.678 is £4.68 to the nearest penny.

In Year 6, children round answers to the accuracy a question asks for. When a fraction gives a decimal that goes on for ever, like a third, they round it, often to three decimal places: a third is about 0.333 and two thirds is about 0.667. Fractions to decimals shows where these come from.

Using rounding to estimate and check answers

Rounding is most useful for checking. From Year 5, children round the numbers in a calculation to check their answer is about the right size. For 4,872 + 3,129, round each to the nearest 1,000: 5,000 + 3,000 = 8,000. The exact answer, 8,001, is close, so it's probably right. If a column addition came out at 80,001, the estimate would catch it.

Sometimes the situation decides which way to round. If 30 people need tents that hold 4, the answer has to round up, not to the nearest. Our guide to short division explains what to do with remainders.

At secondary school: significant figures

Rounding to significant figures is taught at key stage 3, not at primary. The national curriculum says that in Year 6 children round to the nearest 10, 20, 50 and so on, but not to a number of significant figures.

Significant figures count from the first digit that isn't zero. 4,872 to 1 significant figure is 5,000, and to 2 significant figures is 4,900. For small numbers, the zeros at the start don't count: 0.0456 to 2 significant figures is 0.046.

Common rounding mistakes

• Looking at the wrong digit. To round 8,681 to the nearest 100, look at the tens digit (8), not the ones (1).
• Leaving out the zeros. 8,681 to the nearest 100 is 8,700, not 87. The zeros keep the number the right size.
• Rounding in a chain. 3,449 to the nearest 1,000 is 3,000, not 4,000.
• Rounding down "to the digit". 347 to the nearest 10 is 350, not 340. Rounding isn't the same as chopping off the end.
• Losing the zero in decimals. 2.96 to 1 decimal place is 3.0, not 2.9.

How to help at home

• Round prices in the shop. "This is £2.95, so about how much?" Then add up a few rounded prices to estimate the total.
• Use a number line. Draw one from 340 to 350 and ask where 347 goes and which end it's nearer.
• Ask "about how many?" about the miles on a road sign, pages in a book or people at a match.
• Check answers together. Before a sum, ask for an estimate. After it, ask if the answer is close.

Practice questions

1. Round 74 to the nearest 10.
2. Round 3,456 to the nearest 100.
3. Round 6,500 to the nearest 1,000.
4. Round 5.8 to the nearest whole number.
5. Round 7.342 to 1 decimal place.
6. Round 0.6666 to 2 decimal places.

Answers

1. 70
2. 3,500
3. 7,000 (exactly halfway, so round up)
4. 6
5. 7.3
6. 0.67