Perform the following calculations and provide your answers with the correct number of significant figures: a. 0.1886 × 12 b. 2.995 - 0.16685 c. 910 × 0.18945
Physics · High School · Thu Feb 04 2021
Answered on
Answer: a. When multiplying numbers, the result should have the same number of significant figures as the number with the fewest significant figures from those being multiplied. The number 0.1886 has 4 significant figures, and the number 12 has 2 significant figures (assuming it's not a measured value with implied precision like 12.0 or 12.00 which would have 3 or 4 significant figures respectively), so the result should be reported with 2 significant figures.
0.1886 × 12 = 2.2632, but rounded to 2 significant figures, the answer is 2.3.
b. When subtracting, the result should have the same number of decimal places as the number with the fewest decimal places. The number 2.995 has 3 decimal places, and 0.16685 has 5 decimal places, so our result should have 3 decimal places.
2.995 - 0.16685 = 2.82815, but rounded to 3 decimal places, the answer is 2.828.
c. Like multiplication, the final answer of a multiplication problem should have the same number of significant figures as the number with the fewest significant figures. The number 910 has 3 significant figures (if we consider it as approximately measured or assumed to be an exact number), and 0.18945 has 5 significant figures, so the result should have 3 significant figures.
910 × 0.18945 = 172.3995, but rounded to 3 significant figures, the answer is 172.
Extra: In science and mathematics, significant figures are important because they reflect the precision of a measurement or calculation. The rules for significant figures when doing operations are meant to ensure that the precision isn't falsely indicated to be better than the measurements allow.
When addition or subtraction is performed, the result's precision is limited by the term that has the least precision in decimals—the operation cannot be more precise than the least precise measurement.
On the other hand, multiplication and division results are limited by the number of significant figures in the term that has the fewest significant figures. This is because these operations scale the numbers and the resulting precision is proportional to the least precise term.
It is essential for students to grasp the rules for significant figures, as they are commonly used in laboratory measurements and scientific calculations to communicate precision and accuracy of the results.