Significant Figures

in Calculations

A calculated answer cannot be more precise than the least precise measurement from which it was calculated.

The answer must be rounded to the same number of sig fig as least precise number.

2860+9513811

3810

2800+9513751

3800

Rules for Rounding Calculated Answers:

1. When adding or subtracting measurements, the answer should be rounded to the same number of decimal places as the measurement with the least number of decimal places.

55.4598 g + 64.23 g = 119.6898 g = 119.69 g

When working with whole numbers, the answer should be rounded so that the final significant digit is in the same place as the leftmost uncertain digit.

558 g + 60 g = 618 g = 620 g

2. When multiplying or dividing two measurements, round the answer to the same number of significant figures as the measurement with the least number of significant figures.

3.86 cm x 2.2 cm = 8.492 cm2 = 8.5 cm2

8.3 g + 9.5 g + 7.72 g =

25.52 g

25.5 g

Example:

225 cm x 0.50 cm =

112.5 cm2

110 cm2

Example:

2.030 L + 3.1851 L + 2.00 L =

7.2151 L

7.22 L

Example:

58 m ÷ 20 s =

2.9 m/s

3 m/s

Example:

45.3 mg + 17 mg + 33.12 mg =

95.42 mg

95 mg

Example:

0.0361 m - 0.01 m =

0.0261 m

0.03 m

Example:

28590 km ÷ 30. hr =

965 km/hr

960 km/hr

Example:

2.5 x 104 m ÷ 7 x 10-6 s = 0.3571428 x 1010 m/s

0.4 x 1010 m/s

Example:

4 x 109 m/s

7.50 x 108 mL + 2.8 x 109 mL =

3.550 x 109 mL

3.6 x 109 mL

Example:

0.750 x 109 mL + 2.8 x 109 mL =

7.50 x 108 ns + 2.8 x 109 ns =

35.50 x 108 ns

3.6 x 109 ns

Example:

7.50 x 108 ns + 28 x 108 ns=

36 x 108 ns

WHITEBOARD PRACTICE

9.44 m x 7.9 m =

74.576 m2

75 m2

23.06 µg + 58.1851 µg + 44.0 µg =

125.2451 µg

125.2 µg

7.00 x 103 cm x 4.2 x 10-8 cm=

29.4 x 10-5 cm2

29 x 10-5 cm2

2.9 x 10-4 cm2

890 kg - 45 kg =

845 kg

840 kg

96510 g ÷ 500 cm3 =

193.02 g/cm3

200 g/cm3

73 pm + 41.930 pm + 67.60 pm =

182.53 pm

183 pm

4.244 x 105 dm - 1.9 x 104 dm=

4.054 x 105 dm

4.05 x 105 dm

4.244 x 105 dm - 0.19 x 105 dm=

25.0 g ÷ 0.40 mL =

62.5 g/mL

62 g/mL

654 L + 300. L + 84.6 L =

1038.6 L

1039 L

2.83 x 10-9 m ÷ 5.7 x 10-8 s =

0.4964912 x 10-1 m/s

0.50 x 10-1 m/s

5.0 x 10-2 m/s