Arithmetic of Significant Figures

Transcript

Arithmetic of Significant Figures Different rules apply to addition and subtraction, and to multiplication and division. ADDITION AND SUBTRACTION The final answer should retain the same number of decimal places as the quantity with the fewest decimal places, after all quantities are expressed in the same unit. Example: 12.11 + 18.0 + 1.013 = 31.123 18.0 has only 1 decimal place. Final answer = 31.1 Example: 15.67 − 3.2 = 12.47 3.2 has only 1 decimal place. Final answer = 12.5 MULTIPLICATION AND DIVISION The final answer should retain the same number of significant figures as the measured quantity with the fewest significant figures. Example: 12.5 / 3.42 = 3.654… Both values have 3 significant figures. Final answer = 3.65 QUESTION 1: Evaluate 4.237 / 2.51 4.237 / 2.51 = 1.688047… 4.237 has 4 significant figures. 2.51 has 3 significant figures. The final answer must have 3 significant figures. Answer = 1.69 QUESTION 2: Evaluate 12.9 g − 7.86 g 12.9 g − 7.86 g = 5.04 g 12.9 has 1 decimal place. 7.86 has 2 decimal places. The answer must have 1 decimal place. Answer = 5.0 g QUESTION 3: Evaluate 24.36 + 0.0623 + 256.2 24.36 + 0.0623 + 256.2 = 280.6223 The numbers have 2, 4 and 1 decimal places respectively. The final answer must have 1 decimal place. Answer = 280.6 Keep extra digits during calculations and round only the final answer.