significant figures in calculations
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Significant Figures In Calculations
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 =
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)
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.
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.
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.
5. 150.00 g H2O + 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.
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.
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.
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.
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.
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.
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
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 cm1 sig. fig
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 cm1 sig. fig
0.00003 g X 727.0 g =
14.
0.021811 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.
5003 mL / 3.78 mL =
15.
1323.544974 mL3 sig. fig
1320 mL
Remember: When multiplying and dividing, limit and round to the least number of significant figure in any of the factors.
3.44 kg (3.440 kg X 5 kg)
16.
0.2 kg1 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.
=
400.00 m2.30 m
17.
173.9130435 m3 sig. fig.
174 m
Remember: When multiplying and dividing, limit and round to the least number of significant figure in any of the factors.
=
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.
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?
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
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?
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.
Significant FiguresPage 21 Answers
0.0299 ml140 000 m
1280 cm
0.988 g
2475.0 kg0.2 mm23480 ml
3.12 L
162.2 ml20.0 cg
3.9 dm
7.32 mm
5.8 dm
0.899 L19.8 cm
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