1. What are they and why and when are they used?
Significant Figures
What are they and why and when are they used?

2. What are significant figures?
Significant figures are the digits in a number that originate from a proper measurement. That is all of the certain digits and the one uncertain digit in a measurement.

3. What is the difference between these two measurements….2 3
2.3 cm
2.30 cm 2 3

4. Rules for significant figures
All digits 1-9 are significant
Ex: 134 has 3 sig figs
Zeros between significant figures are significant
Ex: has 4 sig figs
Leading zeros are never significant
Ex: has 2 sig figs
Trailing zeros are only significant if the number contains a decimal point
Ex: has 4 sig figs
Ex: 1200 has 2 sig figs

5. How many sig figs in each number?
_____
_____
_____
_____
_____
1.03 x 105 _____ 4 3 2 5

6. Round the following to 3 sig figs
________
________
________
3.245 x 105 ________
________
________
125000
2.94
35.0
3.25 x 105
31Ō00 Or
3.10 x 104

7. Sig Figs and Scientific Notation
When changing a number from standard notation to scientific notation, be sure to maintain the same number of significant digits
Example:
becomes 3.9 x 105
31.0 becomes 3.10 x 101
3Ō000 becomes 3.0 x 104

8. Sig Figs and Metric Conversions
When using dimensional analysis to convert metric units, be sure to maintain the same number of significant digits as the original measurement.
Example: convert 2500 mm  m
2500mm m
x = 2.5 m mm
This is a conversion factor and not a
measurement therefore it does not
count in the sig figs

9. What happens when you need to perform calculations with measurements?
The result of your calculation is only as significant as the measurements involved
You must follow 2 rules for all calculations involving measurements and significant figures

10. Addition and Subtraction
When adding or subtracting, perform the operation as usual, but restrict your result by rounding to the least precise measurement.
0.95 last digit in the hundredths place
last digit in the ten thousandths place
0.9653
Round to the hundredths place
Answer is 0.97

11. Try these… 3.009 - 0.08 ----------- 99.99 + 1.1 789.225 + 90.08A B D C
3.009
- 0.08
99.99
+ 1.1 70
2.93
101.1
879.31 60

12. Multiplication and Division
When multiplying or dividing, perform the operation as usual, but restrict your result by rounding to the smallest number of significant digits.
0.95 This number has 2 sig figs
x This number has 3 sig figs
Round the answer to 2 sig figs
The answer is 0.20

13. Try these… 3.009 ----------- 2.08 (99.99)(1.1)= 789.225A C
3.009
2.08
(99.99)(1.1)=
1.45
110 B D
90.08
(70)(9.002)=
8.761
600

14. REMEMBER… We will be using significant figures throughout the course
Remember that not all calculations involve measurements. Significant digit rules only apply to calculations involving measurements. They are not involved in calculations involving conversion factors.