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

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 g g = g = 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 cm x 2.2 cm = cm 2 =8.5 cm 2

8.3 g g g = g 25.5 g Example:

225 cm x 0.50 cm = cm cm 2 Example:

2.030 L L L = L 7.22 L Example:

58 m ÷ 20 s = 2.9 m/s 3 m/s Example:

45.3 mg + 17 mg mg = mg 95 mg Example:

m m = m 0.03 m Example:

28590 km ÷ 30. hr = 965 km/hr 960 km/hr Example:

2.5 x 10 4 m ÷ 7 x s = x m/s 0.4 x m/s Example: 4 x 10 9 m/s

7.50 x 10 8 mL x 10 9 mL = x 10 9 mL 3.6 x 10 9 mL Example: x 10 9 mL x 10 9 mL =

7.50 x 10 8 ns x 10 9 ns = x 10 8 ns 3.6 x 10 9 ns Example: 7.50 x 10 8 ns + 28 x 10 8 ns= 36 x 10 8 ns

WHITEBOARD PRACTICE

9.44 m x 7.9 m = m 2 75 m 2

23.06 µg µg µg = µg µg

7.00 x 10 3 cm x 4.2 x cm= 29.4 x cm 2 29 x cm x cm 2

890 kg - 45 kg = 845 kg 840 kg

96510 g ÷ 500 cm 3 = g/cm g/cm 3

73 pm pm pm = pm 183 pm

4.244 x 10 5 dm x 10 4 dm= x 10 5 dm 4.05 x 10 5 dm x 10 5 dm x 10 5 dm=

25.0 g ÷ 0.40 mL = 62.5 g/mL 62 g/mL

654 L L L = L 1039 L

2.83 x m ÷ 5.7 x s = x m/s 0.50 x m/s 5.0 x m/s