What answer should be reported, with the correct number of significant figures, for the following calculation?
[(42.00 − 40.914) ⋅ (25.739 − 25.729)] / [(11.50⋅1.001) + (0.00710 ⋅ 700.)]

• A. 7.0 x 10^-4
• B. 6.67 x 10^-4
• C. 6.70 x 10^-4
• D. 6.7 x 10^-4
• E. 6.75 x 10^-4

Answer: (D)

Verified step by step guidance

1. Identify the number of significant figures in each measurement involved in the calculation. For subtraction and addition, the result should have the same number of decimal places as the measurement with the fewest decimal places. For multiplication and division, the result should have the same number of significant figures as the measurement with the fewest significant figures.
2. Perform the subtraction in the numerator: (42.00 - 40.914). Note that 42.00 has 2 decimal places, and 40.914 has 3 decimal places. The result should be rounded to 2 decimal places.
3. Perform the subtraction in the numerator: (25.739 - 25.729). Both numbers have 3 decimal places, so the result should also have 3 decimal places.
4. Perform the multiplication in the denominator: (11.50 * 1.001). 11.50 has 4 significant figures, and 1.001 has 4 significant figures, so the result should have 4 significant figures.
5. Perform the multiplication in the denominator: (0.00710 * 700.). 0.00710 has 3 significant figures, and 700. has 3 significant figures, so the result should have 3 significant figures. Then, add the results from the two multiplications in the denominator, ensuring the final result has the correct number of significant figures based on the rules for addition.