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Rule 1: When multiplying and dividing, limit and round to the least number of significant figure in any of the factors. Example 1: 39.0 mm X 385 mm X 55 mm = 825,825.00 mm (calculator answer) The answer is expressed as 830 000 or 8.3 X 105 since 55 mm has two significant figures. Rule 2: When adding and subtracting, limit and round your answer to the least number of decimal places in any of the numbers that make up your answer. Example 2: 643.40 mL + 40.0 mL + 55.001 mL = 738.40 mL (calculator answer) The answer is expressed as 738.4 mL since 40.0 mL has only one decimal place. Carry out the following calculations expressing your answers to the correct number of significant figures. Assume that all numbers are measured quantities. 1. 0.742mL + 0.0259mL = 0.7679mL (calculator answer) 0.768mL (correct answer) The first value only had three decimal places, whereas the second had four. Remember: When adding and subtracting, limit and round your answer to the least number of decimal places in any of the numbers that make up your answer. 2. 4.00 g – 3.5 g = 0.50 g (calculator answer) 0.5 g (correct answer) There is only one decimal place in the second value, whereas the first had two. Remember: When adding and subtracting, limit and round your answer to the least number of decimal places in any of the numbers that make up your answer. 3. 22.1 ml + 33.2 ml + 224.08 ml = 279.38 mL 279.4 (correct answer) (calculator answer) There is only one decimal place in the first and second value, where as the third had two. Remember: When adding and subtracting, limit and round your answer to the least number of decimal places in any of the numbers that make up your answer. 4. 35.601 g – 34.1 g = 1.501 g (calculator answer) 1.5 g (correct answer) There is only one decimal place in the second value, whereas the first had three. Remember: When adding and subtracting, limit and round your answer to the least number of decimal places in any of the numbers that make up your answer. 5. 150.00 g H2O + 0.507 g salt 150.507 g solution (calculator answer) 150.51 g sol. (correct answer) There are two decimal place in the first value, whereas the second had three. Remember: When adding and subtracting, limit and round your answer to the least number of decimal places in any of the numbers that make up your answer. 6. 67.5 cm - 0.009 cm= 67.491 cm (calculator answer) 67.5 cm (correct answer) There is only one decimal place in the first value, whereas the second had three. Remember: When adding and subtracting, limit and round your answer to the least number of decimal places in any of the numbers that make up your answer. 7. 0.008 mL + 0.05 mL = 0.058 mL (calculator answer) 0.06 mL (correct answer) There are two decimal place in the second value, whereas the first had three. Remember: When adding and subtracting, limit and round your answer to the least number of decimal places in any of the numbers that make up your answer. 8. 250.001 g + 2.000 g + 5000.00 g = 5252.001 g (calculator answer) 5252.00 g (correct answer) There is no decimal place 250001. Remember: When adding and subtracting, limit and round your answer to the least number of decimal places in any of the numbers that make up your answer. 9. 4.60 L + 3 L = 7.6 L (calculator answer) 8 L (correct answer) There is no decimal place on the second value. Remember: When adding and subtracting, limit and round your answer to the least number of decimal places in any of the numbers that make up your answer. 10. 200 mm - 87.3 mm = 112.7 mm (calculator answer) 113 mm (correct answer) There is no decimal place on the first value. Remember: When adding and subtracting, limit and round your answer to the least number of decimal places in any of the numbers that make up your answer. 11. 13.7 cm X 2.5 cm = 34.25 cm 34 cm Remember: When multiplying and dividing, limit and round to the least number of significant figure in any of the factors. 12. 300 cm X 2.88 cm = 864 cm 900 cm Remember: When multiplying and dividing, limit and round to the least number of significant figure in any of the factors. 13. 89 cm _________ = 0.988888889 cm 1 sig. fig 90 cm 1 cm Remember: When multiplying and dividing, limit and round to the least number of significant figure in any of the factors. 14. 0.00003 g X 727.0 g = 0.02181 0.02 g Remember: When multiplying and dividing, limit and round to the least number of significant figure in any of the factors. 15. 5003 mL / 3.78 mL = 1323.544974 mL 1320 mL Remember: When multiplying and dividing, limit and round to the least number of significant figure in any of the factors. 16. 3.44 kg = 0.2 kg (3.440 kg X 5 kg) 0.2 kg Remember: When multiplying and dividing, limit and round to the least number of significant figure in any of the factors. 17. 400.00 m 2.30 m = 173.9130435 m 174 m Remember: When multiplying and dividing, limit and round to the least number of significant figure in any of the factors. 18. 350.00 cm X 0.00072 cm = 0.252 cm 0.25 cm Remember: When multiplying and dividing, limit and round to the least number of significant figure in any of the factors. 19. A piece of metal is found to have a mass of 1.201 grams. What would be the total mass, in grams of 4002 identical pieces of metal? 19. 1.201 g X 4002 g = 4806.402 g 4806 g Remember: When multiplying and dividing, limit and round to the least number of significant figure in any of the factors. 20. A piece of glass is found to have a thickness of 0.122 mm. What would be the total thickness of 5.0 identical pieces of glass? 20. 0.122 mm X 5.0 = 0.61 mm 0.61 mm Remember: When multiplying and dividing, limit and round to the least number of significant figure in any of the factors. Significant Figures Page 21 Answers 0.0299 ml 140 000 m 1280 cm 0.988 g 2475.0 kg 0.2 mm 23480 ml 3.12 L 162.2 ml 20.0 cg 3.9 dm 7.32 mm 5.8 dm 0.899 L 19.8 cm