How Many Significant Figures When Subtracting
When performing subtraction in scientific calculations, it is crucial to consider the number of significant figures in the result. The concept of significant figures is essential in maintaining the accuracy and precision of measurements and calculations. In this article, we will discuss how to determine the number of significant figures when subtracting.
Understanding Significant Figures
Significant figures represent the digits in a number that are known with certainty, plus one uncertain digit. In other words, they indicate the level of precision in a measurement. There are several rules to follow when determining the number of significant figures:
1. All non-zero digits are significant.
2. Zeros between non-zero digits are significant.
3. Leading zeros (zeros before the first non-zero digit) are not significant.
4. Trailing zeros (zeros after the last non-zero digit) are significant if they are after a decimal point.
Subtraction and Significant Figures
When subtracting numbers with different numbers of significant figures, the result should have the same number of significant figures as the number with the fewest significant figures. This rule is known as the “rule of the least significant figure.”
For example, consider the following subtraction problem:
15.2 – 12.9 = 2.3
In this case, the number 12.9 has two significant figures, while the number 15.2 has three significant figures. Therefore, the result, 2.3, should have two significant figures, as it is determined by the number with the fewest significant figures.
Exceptions to the Rule
While the rule of the least significant figure generally applies, there are exceptions. If the numbers being subtracted have different decimal places, the result should have the same number of decimal places as the number with the fewest decimal places.
For example:
15.20 – 12.9 = 2.30
In this case, the number 15.20 has three decimal places, while the number 12.9 has one decimal place. The result, 2.30, has two decimal places, as it is determined by the number with the fewest decimal places.
Conclusion
Understanding how many significant figures to use when subtracting is vital for maintaining the accuracy of scientific calculations. By following the rules of significant figures and the rule of the least significant figure, you can ensure that your results are precise and reliable. Always remember to consider the number of significant figures and decimal places when performing subtraction to achieve the best possible accuracy in your calculations.
