Assignment 1.5: Calculate the answer to the appropriate number of significant figures.

• 0.31 + 0.1                             (b) 658.0 + 23.5478 + 1345.29      (c) 8 × 7

(d) 0.9935 × 10.48 × 13.4 (e) 5.5/1.1                                  (f) (73.2 + 18.72 × 6.1)/3.4

Solution

• 31 + 0.1 = 0.41. See the precisions of both numbers and round off. 0.1 is less precise than 0.31 as it has one digit after decimal point. So round off keeping one digit after the decimal point in the answer. Answer = 0.4
• 0 + 23.5478 + 1345.29 = 2026.8378. Again 658.0 has one digit after the decimal point which is minimum of all. Retain one digit after the decimal point and drop the rest. Answer = 2026.8
• 8 × 7 = 56. The rule for multiplication is when two quantities are multiplied the result has the same number of sig figs as the quantity with smallest number of sig figs. Here both numbers have the same number of sig figs (one). The answer is rounded off to one digit. Answer = 60 = 6 × 101.
• 9935 × 10.48 × 13.4 = 139. 519192. Now 13.4 has the least number of significant figures, three. Therefore, the result is rounded off to three sig figs. Answer = 140 = 1.40 × 102.
• 5.5/1.1 = 5. Both the input numbers have 2 significant figures. Therefore, the answer should be rounded off to two sig figs. Answer = 5 = 5.0
• (73.2 + 18.72 × 6.1)/3.4. First solve the numerator.

73.2 + 18.72 × 6.1 = 73.2 + 114.192 = 187.392 (BODMAS). Now carry out the division. (73.2 + 18.72 × 6.1)/3.4 = 187.392/3.4 = 55. 11529411764706. Now in the division, 3.4 has the least number of significant numbers. The rule for finding the significant figures in division is that round off the answer so that it has the same number of sig figs as the sig figs in the number with least number of sig figs. Therefore, answer = 55