Question

Calculate the percentage of error and answer using the appropriate significant figures/digits of precision.

1. (3.209832−3.1415926)/3.1415926×100%
2. (273.15−273.13)/273.15×100%
3. (38−37)/37×100%

Please show all steps!

a) 2.17%, 0.02%, 2.70%

b) 2.17%, 0.02%, 27.03%

c) 2.18%, 0.03%, 2.70%

d) 2.18%, 0.03%, 27.03%

Answer 1

To calculate the percentage of error with appropriate significant figures, subtract the numerical values, divide by the original value, multiply by 100%, and then round to the number of significant figures determined by the least precise value. Answers include 2.17% for the first calculation, 0.01% for the second calculation, and 2.70% for the third calculation.

Step-by-step explanation:

The student is asked to calculate the percentage of error for three different scenarios and report them with appropriate significant figures. Here’s how to solve each part of the question:

1. Calculate the percentage of error for (3.209832−3.1415926)/3.1415926×100%: The difference between 3.209832 and 3.1415926 is 0.0682394. Dividing by 3.1415926 and then multiplying by 100 gives 2.1721765%. This answer is rounded to three significant figures, which is 2.17%.
2. Calculate the percentage of error for (273.15−273.13)/273.15×100%: The difference is 0.02. Dividing by 273.15 and multiplying by 100 gives 0.007320169%. This answer is rounded to two significant figures, which is 0.0073% or 0.01% when expressed with the appropriate significant figure accuracy.
3. Calculate the percentage of error for (38−37)/37×100%: The difference is 1. Dividing by 37 and multiplying by 100 gives 2.7027027%. This answer is rounded to three significant figures, which is 2.70%.

Therefore, the answers with the correct significant figures are: 2.17%, 0.01%, and 2.70%. Comparing these results with the given options, option (a) is the closest, but has a slight discrepancy in the second calculation due to significant figures rounding.