How to Determine Significant Figures When Dividing
When performing calculations in scientific and engineering fields, it is crucial to understand how to determine significant figures when dividing. Significant figures are the digits in a number that carry meaning in terms of precision. They help to convey the level of accuracy of a measurement or calculation. In this article, we will discuss the rules and methods for determining significant figures when dividing.
Rules for Determining Significant Figures in Division
1. Identify the Significant Figures in Each Number: The first step in determining significant figures when dividing is to identify the significant figures in each of the numbers involved in the division.
2. Use the Least Number of Significant Figures: The result of a division should have the same number of significant figures as the number with the least number of significant figures. For example, if you are dividing 123.4 by 5.6, the result should have two significant figures because 5.6 has only two significant figures.
3. Consider Zeros: Zeros before the first non-zero digit are not significant, but zeros between non-zero digits or after the decimal point are significant. For instance, in the number 0.0045, there are two significant figures.
4. Round the Result: If the last digit in the result is a 5 or higher, round up. If it is a 4 or lower, round down. For example, if you divide 23.45 by 6.78 and get 3.439, round the result to 3.4 because the last digit is 9.
5. Maintain the Decimal Place: If the original numbers have different numbers of decimal places, the result should have the same number of decimal places as the number with the fewest decimal places. For instance, if you divide 12.345 by 0.56, the result should have two decimal places because 0.56 has two decimal places.
Examples of Determining Significant Figures in Division
Let’s consider a few examples to illustrate how to determine significant figures when dividing:
1. Example 1: Divide 25.6 by 4.8.
– Significant figures in 25.6: 3
– Significant figures in 4.8: 2
– Result: 5.3 (rounded to two significant figures)
2. Example 2: Divide 0.0032 by 0.16.
– Significant figures in 0.0032: 1
– Significant figures in 0.16: 2
– Result: 0.02 (rounded to two significant figures)
3. Example 3: Divide 123.4 by 5.6.
– Significant figures in 123.4: 4
– Significant figures in 5.6: 2
– Result: 22 (rounded to two significant figures)
By following these rules and methods, you can determine the correct number of significant figures when dividing in scientific and engineering calculations. This will help you maintain the accuracy and precision of your results.
