Now that you have learned the importance of significant figures, next you will learn how we determine the correct number of significant figures to use when we are performing calculations with our measurements.
When performing calculations involving measured numbers, the calculated answers often appear to have more significant figures than are really justified. For example, dividing 125 by 307 on a calculator gives 0.4071661238 … to an infinite number of digits. But the digits in this answer do not have practical meaning, especially since you are starting with numbers that have only three significant figures each. The answers to calculations like this are rounded to maintain the correct number of significant figures.
When performing mathematical operations, there are two rules for limiting the number of significant figures in an answer-- one rule is for multiplication and division, and another rule is for addition and subtraction, as summarized in this table.
| Multiplication & Division | The answer cannot have more SF than either of the original numbers. |
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| Addition & Subtraction | The answer cannot be more precise (have more decimal places) than either of the original numbers. |
Why do we need to round answers when performing calculations with measured numbers?
| Your Responses | Sample Answers |
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To make sure the answer reflects the precision of the original measurements. |
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