When multiplying and dividing significant figures, it is crucial to understand the rules that govern the number of significant figures in the final answer. Significant figures, also known as significant digits, represent the accuracy of a measurement and are essential in scientific calculations. Following the correct rules for significant figures ensures that the results of calculations are reliable and consistent with the precision of the original data.
In multiplication, the rule for determining the number of significant figures in the final answer is straightforward. The result should contain the same number of significant figures as the measurement with the fewest significant figures. For example, if you multiply 3.45 (with three significant figures) by 2.1 (with two significant figures), the final answer should have two significant figures, as 2.1 is the measurement with the fewest significant figures. Thus, the product would be 7.2, rounded to two significant figures.
When dividing, the rule is similar, but the process may require a bit more attention. The result should have the same number of significant figures as the measurement with the fewest significant figures. For instance, if you divide 3.45 (with three significant figures) by 2.1 (with two significant figures), the final answer should have two significant figures. In this case, the result would be 1.65, which should be rounded to 1.7, maintaining two significant figures.
It is important to note that trailing zeros in a number are significant only if they are measured or known to be accurate. For example, in the number 0.0200, all the zeros are significant because they represent the precision of the measurement. However, if the number is 200, the trailing zeros are not significant because they are merely placeholders.
When performing calculations with significant figures, always follow these guidelines:
1. Identify the number with the fewest significant figures in the calculation.
2. Round the final answer to the same number of significant figures as the number identified in step 1.
3. Pay attention to trailing zeros and determine their significance based on the context of the measurement.
By adhering to these rules, you can ensure that your calculations with significant figures are accurate and reliable. This is particularly important in scientific research, engineering, and other fields where precise measurements and calculations are crucial for the success of the project.
