Perform the following mathematical operation, and report the answer to the correct number of significant figures.
[tex]$0.0030 \times 8.65=[?]$[/tex]
Answer (2)
Multiply the two numbers: 0.0030 × 8.65 = 0.02595 .
Identify the number of significant figures in each number: 0.0030 has two, and 8.65 has three.
Round the result to the least number of significant figures, which is two.
The final answer is 0.026 .
Explanation
Understanding the Problem We are asked to multiply two numbers, 0.0030 and 8.65 , and report the answer to the correct number of significant figures. The number of significant figures in a multiplication is determined by the number with the fewest significant figures.
Identifying Significant Figures The number 0.0030 has two significant figures. The leading zeros are not significant, but the trailing zero is. The number 8.65 has three significant figures.
Performing the Multiplication When we multiply the two numbers, we get 0.0030 × 8.65 = 0.02595 .
Rounding to Correct Significant Figures Since the number with the fewest significant figures is 0.0030 with two significant figures, we must round our answer to two significant figures. The first two significant figures in 0.02595 are 2 and 5 . The next digit is 9 , which is greater than or equal to 5 , so we round the 5 up to a 6 .
Final Answer Therefore, the final answer is 0.026 .
Examples
Significant figures are important in many real-world applications, especially in science and engineering. For example, when measuring the dimensions of a rectangular garden to calculate its area, the precision of the measurements affects the accuracy of the area calculation. If the length is measured as 12.3 meters (3 significant figures) and the width as 5.6 meters (2 significant figures), the area should be reported as 69 square meters (2 significant figures), not 68.88 square meters, to reflect the limitations of the least precise measurement. This ensures that the reported result does not imply a higher level of accuracy than the measurements allow.
By multiplying 0.0030 and 8.65 , we find the initial result is 0.02595 . This value must be rounded to two significant figures, resulting in the final answer of 0.026 . Properly reporting significant figures ensures the precision of measurements is accurately conveyed.
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