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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 10 5 since 55 mm has two significant figures.

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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.

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Carry out the following calculations expressing your answers to the correct number of significant figures. Assume that all numbers are measured quantities.

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1. 0.742mL + 0.0259mL = The first value only had three decimal places, whereas the second had four. 0.768mL (correct answer) 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. 0.7679mL (calculator answer)

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2. 4.00 g – 3.5 g = There is only one decimal place in the second value, whereas the first had two. 0.5 g (correct answer) 0.50 g (calculator answer) 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.

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3. 22.1 ml + 33.2 ml + 224.08 ml = There is only one decimal place in the first and second value, where as the third had two. 279.4 (correct answer) 279.38 mL (calculator answer) 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.

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4. 35.601 g – 34.1 g = There is only one decimal place in the second value, whereas the first had three. 1.5 g (correct answer) 1.501 g (calculator answer) 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.

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5. 150.00 g H 2 O + 0.507 g salt There are two decimal place in the first value, whereas the second had three. 150.51 g sol. (correct answer) 150.507 g solution (calculator answer) 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.

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6. 67.5 cm - 0.009 cm= There is only one decimal place in the first value, whereas the second had three. 67.5 cm (correct answer) 67.491 cm (calculator answer) 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.

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7. 0.008 mL + 0.05 mL = There are two decimal place in the second value, whereas the first had three. 0.06 mL (correct answer) 0.058 mL (calculator answer) 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.

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8. 250.001 g + 2.000 g + 5000.00 g = There is no decimal place 250001. 5252.00 g (correct answer) 5252.001 g (calculator answer) 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.

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9. 4.60 L + 3 L = There is no decimal place on the second value. 8 L (correct answer) 7.6 L (calculator answer) 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.

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10. 200 mm - 87.3 mm = There is no decimal place on the first value. 113 mm (correct answer) 112.7 mm (calculator answer) 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.

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11. 13.7 cm X 2.5 cm = 34 cm Remember: When multiplying and dividing, limit and round to the least number of significant figure in any of the factors. 34.25 cm 2 sig. fig

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12. 300 cm X 2.88 cm = 900 cm Remember: When multiplying and dividing, limit and round to the least number of significant figure in any of the factors. 864 cm 1 sig. fig

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13. 89 cm _________ 90 cm 1 cm Remember: When multiplying and dividing, limit and round to the least number of significant figure in any of the factors. = 0.988888889 cm 1 sig. fig

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0.00003 g X 727.0 g = 14. 0.02181 1 sig. fig 0.02 g Remember: When multiplying and dividing, limit and round to the least number of significant figure in any of the factors.

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5003 mL / 3.78 mL = 15. 1323.544974 mL 3 sig. fig 1320 mL Remember: When multiplying and dividing, limit and round to the least number of significant figure in any of the factors.

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3.44 kg (3.440 kg X 5 kg) 16. 0.2 kg 1 sig. fig. 0.2 kg Remember: When multiplying and dividing, limit and round to the least number of significant figure in any of the factors. =

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400.00 m 2.30 m 17. 173.9130435 m 3 sig. fig. 174 m Remember: When multiplying and dividing, limit and round to the least number of significant figure in any of the factors. =

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350.00 cm X 0.00072 cm = 18. 0.252 cm 2 sig. fig 0.25 cm Remember: When multiplying and dividing, limit and round to the least number of significant figure in any of the factors.

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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?

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1.201 g X 4002 g = 19. 4806.402 g 4 sig. fig 4806 g Remember: When multiplying and dividing, limit and round to the least number of significant figure in any of the factors. 4 sig. fig

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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?

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0.122 mm X 5.0 = 20. 0.61 mm 2 sig. fig 0.61 mm Remember: When multiplying and dividing, limit and round to the least number of significant figure in any of the factors.

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Significant Figures Page 21 Answers

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0.0299 ml 140 000 m 1280 cm 0.988 g 2475.0 kg 0.2 mm 23480 ml 3.12 L

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162.2 ml 20.0 cg 3.9 dm 7.32 mm 5.8 dm 0.899 L 19.8 cm

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