1. Warm up: Mass of Object 24.46 g Volume of Water 12.5 mL
Objective: Perform Calculations to the correct number of digits.
The density of an object was found by using water displacement. The following data was collected (this is in packet).
Determine the volume of the object.
Calculate the density of the object.
Mass of Object
24.46 g
Volume of Water
12.5 mL
Volume of Water and Object
16.3 mL

2. RULES FOR DETERMINING SIGNIFICANT FIGURES
Rule #1: Nonzero digits always count as significant figures: 
Examples:
438 g _____ sig fig
26.42 m _____ sig fig
1.7 cm _____ sig fig
2.653 L _____ sig fig

3. Examples: 0.8 g _____ sig fig
Rule #2: Captive zeros always count as significant figures:
Examples:
506 dm _____ sig fig
1005 mL _____ sig fig
kg _____ sig fig
cm _____ sig fig
Rule #3: Leading zeros do not count as significant figures:
0.8 g _____ sig fig
0.06 g _____ sig fig
L _____ sig fig

4. Rule #4: Trailing zeros are significant only if the number contains a decimal point:
Examples:
60 g _____ sig fig
4830 km _____ sig fig
8.0 dm _____ sig fig
1.60 sec _____ sig fig
L _____ sig fig
kg _____ sig fig

5. RULES FOR ROUNDING NUMBERS
If the digit immediately to the right of the last significant figure you want to retain is:
Less than the last significant digit should stay the same.
Example:
Round m to 3 significant figures.
Since the 2 is less than 5, you should round to __________ m

6. Round 42.68 g to 3 significant figures.
5 or greater the last significant figure should increase by 1.
Example:
Round g to 3 significant figures.
Since 8 is greater than 5, you should round to __________ g

7. What Do You Think?
Determine the number of significant figures in each of the following:
a d
b e
c f
Round each of the following to 2 significant figures.
b c
Explain how the measurement 6.2 cm is different from 6.20 cm.

8. CALCULATIONS WITH MEASUREMENTS
Rule #1: Whenever you add or subtract measurements, your answer should have as many DECIMAL PLACES as the measurement with the LEAST number of DECIMAL PLACES.
EXAMPLE: g g = g
31.28 g

9. Rule#2: Whenever you multiply or divide measurements, your answer should have as many SIGNIFICANT FIGURES as the measurement with the LEAST number of SIGNIFICANT FIGURES.
EXAMPLE: cm × 5.5 cm =
7.381 cm2
7.4 cm2

10. Its Your Turn!
Perform the following calculations and record your answer to the correct number of digits.
a – 6.49 =
b x =
c / =

11. Scientific Notation Short hand for writing very large or small numbers
Two parts: Coefficient and Power of 10
A number between 1 and 10 (can include 1 but not 10).
Exponent:
+ exponent
 - exponent

12. Practice Write the following numbers in scientific notation: 41,000
0.0029
60,007,000
123,000,000

13. One Minute Paper
You have one minute to answer these two questions concerning significant figures and calculations with measurements.
What was the most important thing you learned?
What is still muddy? 13