Perform the following mathematical operation and report the answer to the correct number of significant figures. [tex]$3.22 \times 0.17=[?]$[/tex]
Answer (2)
To multiply 3.22 × 0.17 and report the answer to the correct number of significant figures:
Multiply the two numbers: 3.22 × 0.17 = 0.5474 .
Determine the number of significant figures in each number. 3.22 has three, and 0.17 has two.
Round the result to the fewest number of significant figures, which is two.
The final answer is 0.55 .
Explanation
Understanding the Problem We are asked to multiply two numbers, 3.22 and 0.17 , and report the answer to the correct number of significant figures. The number of significant figures in a multiplication is determined by the factor with the fewest significant figures.
Determining Significant Figures The number 3.22 has three significant figures, and the number 0.17 has two significant figures. Therefore, the result of the multiplication should be rounded to two significant figures.
Performing the Multiplication Multiplying the two numbers, we get 3.22 × 0.17 = 0.5474 .
Rounding to Correct Significant Figures Since we need to round the result to two significant figures, we look at the first three digits: 0.547 . Since the third digit is 7 , which is greater than or equal to 5 , we round up the second digit. Thus, 0.5474 rounded to two significant figures is 0.55 .
Examples
When calculating the area of a rectangular garden plot, you might measure the length to be 3.22 meters and the width to be 0.17 meters. Multiplying these values gives the area, but it's important to report the area with the correct number of significant figures to reflect the precision of your measurements. In this case, the area would be approximately 0.55 square meters.
The result of multiplying 3.22 and 0.17 is 0.5474 . However, rounding it to the correct number of significant figures (two) gives 0.55 . The final answer, therefore, is 0.55 .
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