Rounding to significant figures

When we round to n significant figures (where n is an integer), we follow these steps:

1. Find the position of the nth significant figure in the number (see below).
2. Check the digit after that:
   • If less than 5, you are rounding down, so keep the nth significant figure the same.
   • If more than or equal to 5, you are rounding up, so increase the nth significant figure by one (if it is 9, it becomes 0 and you carry 1 to the left, where you do the same).
3. Remove all digits after the nth significant figure. For any digits you remove, if they’re before the decimal point, replace them with zeroes to keep the place value the same.

Finding the nth significant figure

To find the nth significant figure in a number:

• Start counting from the first non-zero digit (this is the 1st significant figure).
• Continue counting each digit (including zeroes) until you reach the nth significant figure.

Examples

Round 0.0045678 to 3 significant figures

• The 3rd significant figure is 6 (the first significant figure is 4, the second is 5, and the third is 6).
• The number after that is 7.
• 7 is more than 5, so we round up and increase the 6 to 7.
• Remove all digits after the 3rd significant figure, giving 0.00457.
• Answer: 0.00457.

Round 12345 to 2 significant figures

• The 2nd significant figure is 2 (the first significant figure is 1, and the second is 2).
• The number after that is 3.
• 3 is less than 5, so we round down and keep the 2 the same.
• Remove all digits after the 2nd significant figure, replacing them with zeroes to keep the place value the same, giving 12000.
• Answer: 12000.

Round 0.09986 to 2 significant figures

• The 2nd significant figure is 9 (the first significant figure is 9, and the second is 9).
• The number after that is 8.
• 8 is more than 5, so we round up and increase the 9 to 10.
• Since 9 becomes 10, we set the 2nd significant figure to 0 and increase the 1st significant figure by 1 (which is also 9) to get 10.
• Now we have 0.100....
• Remove all digits after the 2nd significant figure, giving 0.10.
• Answer: 0.10.

Round 450600 to 3 significant figures

• The 3rd significant figure is 0 (the first significant figure is 4, the second is 5, and the third is 0).
• The number after that is 6.
• 6 is more than 5, so we round up and increase the 0 to 1.
• Now we have 451000.
• Remove all digits after the 3rd significant figure, replacing them with zeroes to keep the place value the same, giving 451000.
• Answer: 451000.

Round 0.09974 to 2 significant figures

• The 2nd significant figure is 9 (the first significant figure is 9, and the second is also 9).
• The number after that is 7.
• 7 is more than 5, so we round up and increase the 9 to 10.
• Since 9 becomes 10, we set the 2nd significant figure to 0 and increase the 1st significant figure by 1 (which is also 9) to get 10.
• Now we have 0.100....
• Remove all digits after the 2nd significant figure, giving 0.10.
• Answer: 0.10.

Note: Make sure you include both significant figures (including the 0) in ? your answer. Even though 0.10 = 0.1, writing 0.10 shows that you have ? rounded to 2 significant figures instead of just 1.

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