Question

Help with both problems please and thank you.

Perform the calculation and record the answer with the correct number of significant figures.

Problem 1. (6.5−5.91)/3.83 =
problem 2. (34.123+2.80)/(98.7654−9.065) =

Although you have correctly performed the calculation, you have not reported your answer with the correct number of significant figures. Use this list of rules for significant figures following subtraction and division to report your answer with the correct number of significant figures.
First, determine the number of significant figures that result from the subtraction. For subtraction, the number of digits after the decimal point of the difference cannot be greater than that of the measurement with the fewest digits after its decimal point.
Then, determine the significant figures following the division step. The number of significant figures in the quotient cannot be greater than that of the measurement with the fewest significant figures.
Do not round your answer until the very end.

Answer 1

Problem 1:
To calculate (6.5 - 5.91) / 3.83:

Step 1: Perform the subtraction: 6.5 - 5.91 = 0.59
Step 2: Divide the result by 3.83: 0.59 / 3.83 = 0.153987995

To report the answer with the correct number of significant figures:
The measurement with the fewest digits after the decimal point is 3.83 (two digits), so the final answer should be rounded to two digits after the decimal point.

Therefore, the answer to problem 1 is approximately 0.15.

Problem 2:
To calculate (34.123 + 2.80) / (98.7654 - 9.065):

Step 1: Perform the addition: 34.123 + 2.80 = 36.923
Step 2: Perform the subtraction: 98.7654 - 9.065 = 89.7004
Step 3: Divide the sum by the difference: 36.923 / 89.7004 = 0.411760634

To report the answer with the correct number of significant figures:
The measurement with the fewest significant figures is 9.065 (four significant figures), so the final answer should be rounded to four significant figures.

Therefore, the answer to problem 2 is approximately 0.4118.

Answer 2

Problem 1:

(6.5 - 5.91) / 3.83

Step 1: Perform the subtraction:

0.59 / 3.83

Step 2: Determine the number of significant figures after the subtraction:

The measurement with the fewest digits after its decimal point is 3.83, which has 2 digits after the decimal point. Therefore, the difference should also have 2 digits after the decimal point.

0.59 / 3.83 ≈ 0.1542

Step 3: Determine the number of significant figures after the division:

The measurement with the fewest significant figures is 0.59, which has 2 significant figures. Therefore, the quotient should also have 2 significant figures.

0.1542 ≈ 0.15 (rounded to two significant figures)

Therefore, the answer to Problem 1 is 0.15.

Problem 2:

(34.123 + 2.80) / (98.7654 - 9.065)

Step 1: Perform the addition and subtraction:

36.923 / 89.7004

Step 2: Determine the number of significant figures after the division:

The measurement with the fewest significant figures is 89.7004, which has 6 significant figures. Therefore, the quotient should also have 6 significant figures.

36.923 / 89.7004 ≈ 0.411651

Step 3: Determine the number of significant figures after considering subtraction:

The measurement with the fewest digits after its decimal point is 36.923, which has 3 digits after the decimal point. Therefore, the quotient should also have 3 digits after the decimal point.

0.411651 ≈ 0.412 (rounded to three decimal places)

Therefore, the answer to Problem 2 is 0.412.