How to round numbers using significant figures

Key points

One way of rounding numbers is to count only the first few digits (usually 1, 2 or 3 figures) that have a value attached to them. This method of rounding is called . It is often used with larger numbers, or very small numbers.
Significant means important, for example a significant event is an important event. In maths a significant figure is an important digit within the number. The most significant figure is the digit that has the highest .
When rounding numbers, the result is less , but easier to use.
There are slightly different approaches when dealing with small or large numbers.

There are steps which can be followed when rounding using significant figures:

Establish what place value column the most is positioned. For example, if rounding to 1 significant figure then identify the digit that is positioned in the highest column.
Refer back to the rules of rounding to decide whether this should be rounded up.
Leave the digit 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).
The rounded value must be a similar size to the original number, so additional zero digits may be needed. For example, 320 to 1 significant figure is 300.
Using place value labels can help identify what degree of accuracy to round to.

Remember: Units are often referred to as ones. Eg, 34 has 3 tens and 4 units, or say 34 has 3 tens and 4 ones.

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For the value of 37,425 – the digit with the highest place value is 3, so this is the 1st significant figure. The digit 7 has the 2nd highest place value in this number, so the 2nd significant figure is 7
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Round 23,817 to 1 significant figure.
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The digit 2 has the greatest place value. This is most significant value and represents the 1st significant figure. It is positioned in the ten thousands column, so 23,817 is rounded to the nearest ten thousand.
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The 2 is left the same because the next digit (3) is less than 5 (rounding down). The digits after the 1st significant figure are replaced with a zero. 23,817 rounded to 1 significant figure is 20,000
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Round 3892 to 2 significant figures.
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The digit 3 has the greatest place value. The digit 8 represents the 2nd significant figure. The digit 8 is positioned in the hundreds column, so 3892 is rounded to the nearest hundred.
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The digit 8 is rounded up to 9 as the next digit (9) is 5 or more (rounding up). The trailing digits after the 2nd significant figure are replaced with two zeros. 3892 rounded to 2 significant figures is 3900

Round 241,529 to 1 significant figure.

Significant figures start at the first non-zero number, so ignore the zeros at the start of the number, but not the ones in between.
Once the most significant figure has been identified the same rules of rounding are applied.
From the first significant figure onwards, all zeros are included. It's only the zeros at the beginning that don't count.

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For the value of 0∙0327, the digit with the highest place value is 3. This is the 1st significant figure. Ignore the place value columns at the beginning containing zero. The 2nd significant figure is the digit in the next place value column which is the 2. The 3rd significant figure is 7
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Round 0∙0472 to 1 significant figure.
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The digit 4 has the greatest place value. This is the first non-zero digit in the value. The 4 is the most significant value and represents the 1st significant figure. The digit 4 is positioned in the hundredths column, so 0∙0472 is rounded to the nearest hundredth. The 4 is rounded up because the next digit (7) is 5 or more.
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The 4 is rounded up to 5. No further digits are included after the 5
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Round 0∙3019 to 2 significant figures.
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The digit 3 has the greatest place value and is the first non-zero digit in the value. The digit zero represents the 2nd significant figure. The 2nd significant figure is positioned in the hundredths column, so 0∙3019 is rounded to the nearest hundredth. The 0 is left the same because the next digit (1) is less than 5 (rounding down).
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There must be two significant digits in the final answer so one zero following the 3 must be included. 0∙3 would have only been rounded to 1 significant figure. 0∙3019 rounded to 2 significant figures is 0∙30

Practise rounding numbers using significant figures in this quiz.

Rounding using significant figures is useful when dealing with extremely large or small numbers where rounding using other methods is not always appropriate.
An engineer may round a measurement to 2 or 3 significant figures because they can’t measure any more accurately.