How Do Significant Figures Work?

We count the number of significant figures in a number by looking at whether or not your number contains leading zeroes.

Rule

Significant Figures

When the number begins with a $0$ , count the number of digits from the first non-zero digit.
When the number doesn’t begin with a $0$ , count all the number’s digits.

Example 1

Significant figures:

1	has 1 significant figure
10	has 2 significant figures
100	has 3 significant figures
$1.0$	has 2 significant figures
$1.00$	has 3 significant figures
$1.000$	has 4 significant figures
$0.00$ 1	has 1 significant figure
$0.00$ 10	has 2 significant figures
$0.00$ 100	has 3 significant figures

Example 2

The distance between your home and the sports hall is $10.5$ miles. The sports hall is $8.1$ miles away from the shop. How far have you traveled if you bike from home to the shop, but you stop by the sports hall on the way? Give your answer with four significant figures.

In this example, you’ll have to add the distances to see how far you’ve traveled. You get

\begin{array}{l} 10.5 miles + 8.1 miles & = 18.6 miles \\ = 18.60 miles \end{array}

10.5 miles + 8.1 miles = 18.6 miles = 18.60 miles

We had to write an additional trailing zero to give our answer four significant figures.

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The Digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9)

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