Maths
What is rounding in maths?
Quick answer
Rounding means replacing a number with a simpler one that is close to it, such as 47 rounded to the nearest ten being 50. It makes numbers easier to work with.
In one sentence
Rounding means swapping an exact number for a nearby "tidy" number, like saying a 58-minute film lasts about an hour.
Explained
Rounding is how we say "roughly". If a school has 487 pupils, people often say "nearly 500". You have rounded 487 to the nearest hundred.
To round, first decide what you are rounding to: the nearest 10, 100, 1000, whole number or decimal place. Then find the two tidy numbers on either side and pick the closer one. Imagine the number as a ball on a hill: past halfway, it rolls forward; before halfway, it rolls back.
mountain
There is a quick rule that does the same job. Look at the digit just to the right of the place you are rounding to:
- If it is 0, 1, 2, 3 or 4, round down (the digit you are rounding stays the same).
- If it is 5, 6, 7, 8 or 9, round up (that digit goes up by one).
Then replace all the digits after it with zeros, or drop them after a decimal point.
Rounding to the nearest 10, 100 or 1000 uses place value: 3,742 to the nearest hundred looks at the tens digit (4), so it rounds down to 3,700. With decimals, 6.38 to the nearest whole number looks at the tenths digit (3), so it becomes 6.
Examples
| Number | Round to | Look at | Answer |
|---|---|---|---|
| 74 | nearest 10 | 4 | 70 |
| 75 | nearest 10 | 5 | 80 |
| 1,350 | nearest 100 | 5 | 1,400 |
| 296 | nearest 10 | 6 | 300 (the 9 tips over) |
| 12.83 | nearest whole | 8 | 13 |
| 0.462 | 2 decimal places | 2 | 0.46 |
Common mistakes
- Looking at the wrong digit. For the nearest 100, look at the tens digit, not the ones.
- Changing the digits that should stay. 4,382 to the nearest 100 is 4,400, not 400 or 4,482.
- Forgetting to carry when a 9 rounds up. 3.97 to one decimal place is 4.0, not 3.10.
- Rounding twice. 1,449 to the nearest 100 is 1,400. Rounding to 1,450 first and then to 1,500 is wrong.
Quick quiz
Rounding
Check what you know with 4 quick questions.
Question 1 of 4
What is 63 rounded to the nearest 10?
Practise it
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Mental maths and rounding practice
For grown-ups
Related topics
Estimation
Estimating means making a sensible guess at an answer, usually by rounding the numbers first. It tells you roughly what to expect and helps you spot mistakes.
Place value
Place value means a digit's value depends on its position in a number. In 352, the 3 is worth 300, the 5 is worth 50 and the 2 is worth 2.
Decimals
Decimals are numbers with a decimal point. Digits after the point show tenths, hundredths and so on, so 2.5 means two and five tenths.
Number line
A number line is a straight line with numbers marked at equal steps, smallest on the left and biggest on the right. It helps you count, compare, add and subtract.
2D shapes
2D shapes are flat shapes with length and width but no thickness, like circles, triangles, squares and hexagons. You can draw them on paper.
3D shapes
3D shapes are solid shapes with length, width and height, like cubes, spheres, cylinders and pyramids. They have faces, edges and vertices.