Perform the following mathematical operation and report the answer to the correct number of significant figures.
[tex]$0.0030 \times 8.65 = \square$[/tex]
Answer (2)
Multiply the two numbers: 0.0030 × 8.65 = 0.02595 .
Determine the number of significant figures: 0.0030 has 2, and 8.65 has 3.
Round the result to the least number of significant figures, which is 2.
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. Significant figures are important because they indicate the precision of a measurement.
Performing the Multiplication First, perform the multiplication: 0.0030 × 8.65 = 0.02595
Determining Significant Figures Next, we need to determine the number of significant figures in each of the original numbers. The number 0.0030 has two significant figures (the leading zeros are not significant), and the number 8.65 has three significant figures. When multiplying or dividing, the result should have the same number of significant figures as the number with the fewest significant figures. In this case, 0.0030 has the fewest significant figures, which is two.
Rounding to Correct Significant Figures Now, we round the result, 0.02595 , to two significant figures. The first two significant figures are 0.025 . Since the next digit is 9 , which is greater than or equal to 5 , we round up the last significant figure. Therefore, 0.02595 rounded to two significant figures is 0.026 .
Final Answer Therefore, the final answer, reported to the correct number of significant figures, is 0.026 .
Examples
Significant figures are crucial in scientific and engineering calculations. For instance, if you're calculating the area of a rectangular garden with a length of 12.5 meters (3 significant figures) and a width of 4.0 meters (2 significant figures), the area should be reported as 50 square meters (2 significant figures), not 50.0 square meters, to reflect the precision of the least precise measurement.
The product of 0.0030 × 8.65 is 0.02595 . When rounded to the correct number of significant figures, the final answer is 0.026 . This answer reflects the precision of the least precise measurement in the multiplication.
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