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Significant Figures

Counting Significant Figures

Atlantic-Pacific Rule: In numbers written with decimal points (present), count significant figures from the left (pacific side). In numbers written without decimal points (absent), count from the right (atlantic side) beginning with the first nonzero digit.

1.  How many significant figures are in each of the following measurements?

a.  0.0370 g. 0.23100

b.  200 h. 23,100

c.  20. i. 23,100.

d.  20.0 j. 7.203

e.  400,900 k. 0.00231

f.  0.00990 l. 2000

Calculating With Significant Figures

When you use measurements in calculations, your answer may only be as exact as your least exact measurement.

Rule for Addition and Subtraction: Round to the fewest decimal places.

2.  Perform the following calculations, and round off your answer correctly:

a.  4.1 cm + 0.07 cm

b.  18.3 m – 11 m

c.  8.120 g – 7.090 g

Rule for Multiplication and Division: Round to the fewest significant figures.

3.  Perform the following calculations, and round off your answer correctly:

a.  4.1 cm x 0.07 cm

b.  7.079 cm / 0.53 s

c.  8.120 m x 7.090 m

Practice Problems: Perform the following calculations and complete the table.

Unrounded Answer / Rounded Answer
4. / 45.71 cm x 0.20 cm
5. / 10.2 m / 0.4 s
6. / 100. mm – 1.6 mm
7. / 4302 g + 0.837 g
8. / 87.3 cm – 1.655 cm
9. / 2.099 g + 0.05681 g
10. / 2.4 g/mL x 15.82 mL
11. / 105.725 g / 39.1 mL

Using an Equation

The ratio of mass to volume for a substance is called its density. This relationship can be expressed by the following equation: D = M/V

Use the density equation given above to solve the following problems. Be sure to round off your answer correctly.

12. What is the density of a sample of mercury that has a mass of 39.60 g and a volume of 9.00 cm3?

13. Granite has a density of 4.67 g/cm3. What is the mass of 50 cm3 of granite?