What are the rules for multiplying and dividing significant figures?
In scientific calculations, the precision of the results is crucial. Significant figures, also known as significant digits, play a vital role in determining the accuracy of a measurement. The rules for multiplying and dividing significant figures are essential for maintaining the precision of the results. Understanding these rules can help you avoid common mistakes and ensure that your calculations are accurate.
Rules for Multiplying Significant Figures
When multiplying 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 multiply 2.5 (with two significant figures) by 1.23 (with three significant figures), the result should be rounded to two significant figures, which is 3.0.
Here are the key rules for multiplying significant figures:
1. Count the significant figures in each number.
2. Perform the multiplication as usual.
3. Round the result to the same number of significant figures as the number with the fewest significant figures.
Rules for Dividing Significant Figures
When dividing 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 divide 2.5 (with two significant figures) by 1.23 (with three significant figures), the result should be rounded to two significant figures, which is approximately 2.0.
Here are the key rules for dividing significant figures:
1. Count the significant figures in each number.
2. Perform the division as usual.
3. Round the result to the same number of significant figures as the number with the fewest significant figures.
Examples of Multiplying and Dividing Significant Figures
Let’s look at some examples to illustrate these rules:
Example 1: Multiply 2.5 (two significant figures) by 1.23 (three significant figures).
Solution: 2.5 x 1.23 = 3.075. Since 1.23 has the fewest significant figures (three), the result should be rounded to two significant figures: 3.0.
Example 2: Divide 2.5 (two significant figures) by 1.23 (three significant figures).
Solution: 2.5 ÷ 1.23 = 2.0806328. Since 1.23 has the fewest significant figures (three), the result should be rounded to two significant figures: 2.1.
By following these rules for multiplying and dividing significant figures, you can maintain the precision of your calculations and ensure that your results are accurate. Remember to always count the significant figures and round the result accordingly.
