1. Objectives
To learn how uncertainty in a measurement arises
To learn to indicate a measurement’s uncertainty by using significant figures
To learn to determine the number of significant figures in a calculated result

2. A. Uncertainty in Measurement
A measurement always has some degree of uncertainty.

3. A. Uncertainty in Measurement
Different people estimate differently.
Record all certain numbers and one estimated number.

4. B. Significant Figures
Significant figures are the meaningful figures in our measurements and they allow us to generate meaningful conclusions
Numbers recorded in a measurement are significant.
All the certain numbers plus first estimated number
e.g cm
We need to be able to combine data and still produce meaningful information
There are rules about combining data that depend on how many significant figures we start with………

5. B. Significant Figures
Rules for Counting Significant Figures
Nonzero integers always count as significant figures.
1457 has 4 significant figures
23.3 has 3 significant figures

6. B. Significant Figures
Rules for Counting Significant Figures
Zeros
Leading zeros - never count significant figures
Captive zeros - always count significant figures
Trailing zeros - count only if the number is written with a decimal point significant figure significant figures significant figures

7. B. Significant Figures
Rules for Counting Significant Figures
Exact numbers - unlimited significant figures
Not obtained by measurement
Determined by counting: 3 apples
Determined by definition: 1 in. = cm

8. How Many Significant Figures?
, x
102
102.0
1.02
1.02 x 104
1.020 x 104
60 minutes in an hour
500 laps in the race

9. B. Significant Figures
- Round off to 1,2,3,4 significant figures

10. B. Significant Figures
Rules for Multiplication and Division
The number of significant figures in the result is the same as in the measurement with the smallest number of significant figures.

11. B. Significant Figures
Rules for Addition and Subtraction
The number of significant figures in the result is the same as in the measurement with the smallest number of decimal places.

12. Rules for Combined Units
Multiplication / Division
When you Multiply or Divide measurements you must carry out the same operation with the units as you do with the numbers
50 cm x 150 cm = 7500 cm2
20 m / 5 s = 4 m/s or 4 ms-1
16m / 4m = 4
Addition / Subtraction
When you Add or Subtract measurements they must be in the same units and the units remain the same
50 cm cm = 200 cm
20 m/s – 15 m/s = 5 m/s

13. Calculate the following
Calculate the following. Give your answer to the correct number of significant figures and use the correct units
11.7 km x km =
12 mm x 34 mm x mm =
14.05 m / 7 s =
108 kg / 550 m3 =
23.2 L + 14 L =
55.3 s s =
16.37 cm – 4.2 cm =
km – km =