Mastering the Essentials- The Comprehensive Guide to Adding and Subtracting Significant Figures
What is the rule for adding and subtracting significant figures?
In scientific calculations, it is crucial to maintain accuracy and precision. One way to ensure this is by adhering to the rules for adding and subtracting significant figures. Significant figures represent the number of digits in a number that are known with certainty, plus one uncertain digit. Understanding these rules is essential for students and professionals in various scientific fields, including chemistry, physics, and engineering.
Rules for Adding Significant Figures
When adding 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. For example, if you add 2.34 (three significant figures) and 0.008 (one significant figure), the result is 2.34 + 0.008 = 2.34. In this case, the result has three significant figures, as 0.008 has the fewest significant figures.
Rules for Subtracting Significant Figures
Subtraction follows a similar rule as addition. 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. For instance, if you subtract 0.021 (two significant figures) from 0.023 (two significant figures), the result is 0.023 – 0.021 = 0.002. Here, the result has two significant figures, as both numbers have the same number of significant figures.
Special Cases
There are a few special cases to consider when dealing with significant figures:
1. Zeroes: Leading zeroes ( zeroes before the first non-zero digit) are not significant. Trailing zeroes ( zeroes after the last non-zero digit) are significant if they are after a decimal point. For example, 0.0045 has two significant figures, while 4500 has three significant figures.
2. Scientific Notation: When performing calculations in scientific notation, the rules for significant figures still apply. For example, if you add 2.34 x 10^3 and 0.008 x 10^3, the result is 2.34 x 10^3 + 0.008 x 10^3 = 2.34 x 10^3. The result has three significant figures, as 0.008 has the fewest significant figures.
3. Rounding: When rounding a number to a specific number of significant figures, ensure that you round the last significant figure correctly. For example, if you have a number with four significant figures, 0.0045, and you need to round it to two significant figures, the result is 0.004. The third significant figure (5) is dropped, and the second significant figure (4) is rounded up to 5.
In conclusion, the rule for adding and subtracting significant figures is to maintain the same number of significant figures as the number with the fewest significant figures. By following these rules, you can ensure accuracy and precision in your scientific calculations.
