Question

Without actually performing the calculations indicated, tell to how many significant digits the answer to the calculation should be expressed. a. \(\frac{(9.7871)(2)}{(0.00182)(43.21)}\) b. \((67.41+0.32+1.98) /(18.225)\) c. \(\left(2.001 \times 10^{-3}\right)\left(4.7 \times 10^{-6}\right)\left(68.224 \times 10^{-2}\right)\) d. (72.15)(63.9)\([1.98+4.8981]\)

Short answer

The number of significant digits for each calculation should be: a. 1 b. 2 c. 2 d. 3

Step-by-step solution

Analyze Calculation a

For the calculation a, we have multiplication and division: \(\frac{(9.7871)(2)}{(0.00182)(43.21)}\). Here we will follow the first rule as mentioned above. The number of significant figures for each term is 5, 1, 3, and 4 respectively. According to rule 1, we take the least number of significant figures and express the answer to that many significant figures which is 1.

Analyze Calculation b

For the calculation b, we have addition in the numerator, and only division: \((67.41+0.32+1.98) /(18.225)\). The result of the numerator addition should follow the second rule. The number of decimal places for numerator terms is 2, 0, and 2 respectively. According to rule 2, the result of the addition should have the same number of decimal places as the term with the least decimal places which is 0. Now we have division, so we will look at the number of significant figures for the numerator result and 18.225. The number of significant figures for numerator result is 2 (with 0 decimal places) and for 18.225 it is 5. According to rule 1, our answer should have the same significant figures as the term with the least significant figures which is 2.

Analyze Calculation c

For the calculation c, we have multiplication only: \(\left(2.001 \times 10^{-3}\right)\left(4.7 \times 10^{-6}\right)\left(68.224 \times 10^{-2}\right)\). The number of significant figures for each term is 4, 2, and 5 respectively. According to rule 1, we will express the answer to the least number of significant figures which is 2.

Analyze Calculation d

For the calculation d, we have multiplication and addition within brackets (72.150)(63.90) \([1.98+4.8981]\). First, we need to find out the number of significant figures for the addition \([1.9800+4.8981]\) within the brackets. The number of decimal places for these terms is 2 and 4 respectively. According to rule 2, we should express the result of the addition with the same number of decimal places as the term with the least number of decimal places which is 2. Next, we have multiplication. The number of significant figures for each term is 4, 3 and 4 (2 decimal places in the addition). According to rule 1, we will express the answer to the least number of significant figures which is 3.