1. Significant Figures in Calculations
Chapter 1 Measurements
Significant Figures in Calculations

2. Every time we state a number it is limited by the accuracy of the measurement.

3. He rushed for about 200 yards…or was it 212 yards or maybe 212.2
I weigh 172 lbs…or is it 172.4lbs or is it lbs.
I have $30,000…or is it $30,134 …or maybe $30,134.25

4. Significant Figures in Measurement
The numbers reported in a measurement are limited by the measuring tool
Significant figures in a measurement include the known digits plus one estimated digit

5. Counting Significant Figures
Number of Significant Figures
38.15 cm 4
5.6 ft 2
65.6 lb ___
m ___
Rule 1: All non-zero digits (1-9) in a measured number are significant (count).

6. Leading Zeros (zeros at the beginning of a number)
Number of Significant Figures
0.008 mm 1
oz 3
lb ____
mL ____
Rule 2: Leading zeros in decimal numbers are not significant (don’t count).

7. “Sandwiched” Zeros Number of Significant Figures 50.8 mm 3 2001 min 4
0.702 lb ____
m ____
Rule 3: Zeros between nonzero numbers
(1-9) are significant (count).

8. Trailing Zeros (zeros at the end of a number)
Number of Significant Figures in yr gal ____ 25,005,000 g ____ Rule 4: Trailing zeros in numbers without decimals are not significant (don’t count), they are serving as place holders. If there is a decimal they are significant (count).

9. Learning Check
1. Which answers contain 3 significant figures? a) b) c) All the zeros are significant in a) b) c) 2.050

10. Solution
1. Which answers contain 3 significant figures? b) c) All the zeros are significant in b) c) 2.050

11. Learning Check a) 22.0 and 22.00 b) 400.0 and 40
3. In which set(s) do both numbers contain the same number of significant figures?
a) and 22.00
b) and 40
c) and 150,000

12. Solution
3. In which set(s) do both numbers contain the same number of significant figures?
c) and 150,000

13. Learning Check
State the number of significant figures in each of the following: m L g m
8. 2,080,000 bees

14. Solution
m L g m ,080,000 bees 3
Timberlake lecture plus

15. Significant Numbers in Calculations
A calculated answer cannot be more precise than the measuring tool.
A calculated answer must match the least precise measurement.
Significant figures are needed for final answers from
1) adding or subtracting
2) multiplying or dividing

16. Adding and Subtracting
The answer has the same number of decimal places as the measurement with the fewest decimal places.
one decimal place
two decimal places
26.54
answer one decimal place

17. Learning Check
In each calculation, round the answer to the correct number of significant figures = a) b) c) = a) b) c) 40.7

18. Solution
= 2) = 3) 40.7
Timberlake lecture plus

19. Multiplying and Dividing
Round (or add zeros) to the calculated answer until you have the same number of significant figures as the measurement with the fewest significant figures.

20. Learning Check 11. 2.19 X 4.2 = a) 9 b) 9.2 c) 9.198
÷ =
a) b) 62 c) 60

21. Solution
X 4.2 = b) ÷ 0.07 = c) 60