Here you will learn about significant figures, how to identify significant figures within a given number and how to round to one significant figure, two significant figures, and three significant figures.

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Students will first learn about significant figures as part of expression and equations in the 8th grade.

Significant figures are each of the digits in a number that are used to express it, to the required degree of accuracy, starting from the first non-zero digit. The first significant figure, or significant digit, of a number is the most important digit because it expresses the size of the number.

To locate a significant figure, you need to find the first non-zero digit. This is the first significant figure. The next digit is the second significant figure and so on.

A significant figure could be to the left of the decimal point or the right of the decimal point.

There are significant figure rules that will help you identify all the significant figures in a given number:

Rounding numbers to significant figures (often abbreviated to sig figs or s.f.), is similar to rounding to a number of decimal places, such as the ones place, tens place, hundreds place, and thousands place.

Identify the correct number of significant figures in the number 405.

The first non-zero digit is the 4 in the hundreds place.

2Starting at the first non-zero digit, count the number of digits that are non-zero numbers or zeros between non-zero digits.

All three digits are either non-zero numbers or have a zero between non-zero digits.

The 4 is the first significant digit, and the 5 is the last significant digit.

Identify the correct number of significant figures in the number 0.037.

The first non-zero digit is the 3 in the hundredths place.

Starting at the first non-zero digit, count the number of digits that are non-zero numbers or zeros between non-zero digits.

The 3 and the 7 are non-zero digits. The 3 is the first significant digit, and the 7 is the last significant digit.

There is a decimal in this number, but no trailing zeros.

Calculate the number of significant figures for the number 0.004500.

The first non-zero digit is the 4 in the thousandths place.

Starting at the first non-zero digit, count the number of digits that are non-zero numbers or zeros between non-zero digits.

The 4 is the first significant digit, and the 5 is the last significant non-zero digit.

There is a decimal present, so the last 2 zeros in the number are trailing zeros.

In order to round to a given number of significant digits:

Round 3,692 to one significant figure (1 \, s.f) .

Locate the significant figure for the degree of accuracy required.

The first non-zero digit is 3, therefore 3 is the first significant figure.

Look at the next digit immediately to the right. When the digit is \bf{5} or more, round up by adding \bf{1} to the previous digit. When the digit is less than \bf{5} , round down by keeping the previous digit the same.

Because 6 is greater than 5, you will round up. Adding 1 to the 3 gives you 4.

When the degree of accuracy is \bf{10} or more, use zeros as place holders.

The first significant figure represents thousands, so you must include three zeros as place holders to make it the correct size.

Round 0.07039 to two significant figures (2 \, s.f.) .

Locate the significant figure for the degree of accuracy required.

The first non-zero digit is the 7, which is the first significant figure; therefore, the 0, at the thousandths place, is the second significant figure.

Look at the next digit immediately to the right. When the digit is \bf{5} or more, round up by adding \bf{1} to the previous digit. When the digit is less than \bf{5} , round down by keeping the previous digit the same.

Because 3 is less than 5, you will round down.

When the degree of accuracy is \bf{10} or more, use zeros as place holders.

It is important to keep the zero after the seven as it must be given to two significant figures.

Note: You will often write very small numbers, such as 0.07039 using standard form (scientific notation).

Round 24.753 to three significant figures (3 \, s.f.) .

Locate the significant figure for the degree of accuracy required.

The first non-zero digit is 2, which is the first significant figure. Therefore, the 7, in the tenths place, is the third significant figure.

Look at the next digit immediately to the right. When the digit is \bf{5} or more, round up by adding \bf{1} to the previous digit. When the digit is less than \bf{5} , round down by keeping the previous digit the same.

Because the number is 5, you will round up. Adding 1 to the 7 gives you 8.

When the degree of accuracy is \bf{10} or more, use zeros as place holders.

You do not need to include any zero place holders after the 8 because there are already three significant figures present.

This significant figures topic guide is part of our series on rounding decimals. You may find it helpful to start with the main rounding decimals topic guide for a summary of what to expect or use the step-by-step guides below for further detail on individual topics. Other topic guides in this series include:

1. Identify the correct number of significant figures in the number 86.09.

Continue counting all non-zero digits and zeros between non-zero digits.

2. Identify the correct number of significant figures in the number 0.0980.

Continue counting all non-zero digits and zeros between non-zero digits.

The zero in the ten thousandths place will also be a significant figure because it’s a trailing zero when there is a decimal present.

3. Which of the following numbers has the fewest significant figures?

The next digit to the right is 6, which is bigger than 5, so you round up.

Adding 1 to 7 gives you 8 and filling in the placeholder zeros gives you 80,000.

The first significant figure is 7 and the second is 8.

The next number to the right is 5, so you round up.

Adding one to the 8 is 9, which gives you 79.

The first significant figure is 5 and the third significant figure is 4.

The next number to the right is 8, which is bigger than 5, so you round up.

Adding 1 to the 4 is 5, which gives you 0.00515.

All non-zero digits are significant figures. Zeros are also significant with the exception of two things:
1) the zero is alone before the decimal point and,
2) the zero is after the decimal point, but before the first non-zero digit.

You will first identify the significant figure that you will round to.
Follow the same rounding steps as you have learned with whole numbers and decimal places. (For example, 5 or more, you add one to the digit of the rounded place. 4 or less, the digit will stay the same).

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