Rounding numbers (decimals)

Key points

Rounded values

When rounding decimals apply the same mathematical rules used when rounding whole numbers.
It is not always possible to give an exact value. When it’s not possible, numbers can be rounded. For example, when Usain Bolt broke the 100 m World Record in August 2009, his time was recorded as an incredible 9.58 seconds. Time is an example of data, meaning that his time of 9.58 seconds has been measured as accurately as possible, but ultimately has been rounded to the nearest one hundredth of a second.
Depending on the context, and the need for , values can be rounded. They can be rounded, for example, to the nearest:
- tenth
- hundredth
- thousandth

Decimal places

Rounding to a desired degree of accuracy means making a number simpler but keeping its value very close to what it was. The result is not exact, but is easier to manage and use.

There are steps which can be followed to decide whether a number should be rounded up or rounded down to a set degree of accuracy.

Identify the position of the decimal place you are rounding to.
Leave it the same if the next digit is less than 5 (this is called rounding down)
But increase it by 1 if the next digit is 5 or more (this is called rounding up)
Using a as a representation is a helpful way of visualising whether a number is closer to one value or another.

Examples

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Decimal places are counted from the decimal point. The number 3 ∙728 is written to three decimal places.
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Round 8∙736 to 2 decimal places. This means starting at 2 digits after the decimal point. Count the digits from the decimal point. The digit 3 is in the second decimal place.
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The next digit is 6. Because 6 is more than 5, the 3 is rounded up. 8∙736 rounded to 2 decimal places is 8∙74
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Round 6∙8279 to 1 decimal place. This means starting at 1 digit after the decimal point. Count the digits from the decimal point. 8 is in the first decimal place.
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The next digit is 2. Because 2 is less than 5, the 8 in the second decimal place is not changed. 6∙8279 to 1 decimal place is rounded down to 6∙8.
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Round 4∙8298 to 3 decimal places. This means starting at 3 digits after the decimal point. Count the digits from the decimal point. 9 is in the third decimal place.
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The next digit after the third decimal place is 8. Because 8 is more than 5, the 9 is rounded up. However, the 9 cannot be rounded up to 10. The number must be rounded to 4∙830
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A number line can often help in rounding numbers. 4∙8298 rounds up to 4∙830 to 3 decimal places, as shown on the number line.

Question

Round 4∙5629 to 2 decimal places.

Practise rounding numbers

Practise rounding decimal numbers in this quiz.

Quiz

Real-world maths

A yellow formula one car passing over the finish line. The photo is is blurry with motion blur. — Image caption,
Formula 1 races are usually timed to 3 decimal places.

Rounding decimal values is used regularly in everyday life.An exact figure or value is not always appropriate to use or becomes difficult to manage effectively, particularly when dealing with continuous data as our ability to measure precisely is limited.

Converting between imperial and metric measurements usually results in values with several decimal places. It is common to round these to deal with more manageable values.
Measuring the time taken to complete a task can only be measured to a certain degree of accuracy so these are usually rounded to 2 or 3 decimal places (or the nearest one hundredth or one thousandth of a second). For example, in a sports events and motor racing.