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Rounding to Significant Figures

Rounding to Significant Figures

The first significant figure in a number is the first non-zero digit in the number (reading from left to right). In the numbers 35, 35985 and 0.00356, the first significant figure is the number 3.

When counting for two or more significant figures, then count the figures after the first significant figure has been found.

When rounding, find the number of significant figures required then check the next digit after the significant figures. If the next digit is less than 5, then round down: if 5 or greater, then round up.

Significant figures are sometimes shown as sf: for example, 3.4 (2sf) means the number is 3.4 to 2 significant figures.

Examples of significant figures:

Number 56 518 4895 23.46 0.456 0.0453
1 significant figure 60 500 5000 20 0.5 0.05
2 significant figures 56 520 4900 23 0.46 0.045
3 significant figures 56 518 4900 23.5 0.456 0.0453

Example 1

In a physics experiment, Emily measured a force of 12.45 Newtons. What was the value of the force to two significant figures?

The first two significant figures are 12: check the next digit (4); this is less than 5 so the number stays as 12. Note that writing 12.0 would be wrong, as this would imply an accuracy of three significant figures.

Answer: 12 Newtons

Example 2

Harry jumped 2564 millimetres in a long jump. What distance was this, rounded to one significant figure?

The first significant figure is a 2. Check the next digit (5): it is 5 or more so round the significant figure up (from 2 to 3).

Answer: 3000 millimetres