1. And Calculating with Significant Digits
Density
And
Calculating with Significant Digits

2. Density – the ratio of an object’s mass to volume. Formula: D = M V
Units:
g/mL (liquid)
g/ cm3 (solid)

3. Density
EVERYTHING has a unique density, therefore density can be used to identify an unknown sample of matter.

4. The density of water = 1.0 g/ml
Will it float or sink?
The density of water = 1.0 g/ml
Anything with a density more than 1.0 g/ml = sinks in water
Anything with a density less than 1.0 g/ml = floats on water

5. Significant Figures in Calculations
Calculated values must be rounded so that they are consistent with the data from which they were calculated.

6. Multiplication and Division
In calculations involving multiplication and division, answers should be rounded so that they contain the same number of significant digits as the measurement with the LOWEST number of significant digits.

7. Examples:
7.55 m x 0.34 m = m2
Should be rounded to 2.6 m2
m / 8.4 m = m2
Should be rounded to 0.29 m2

8. Addition and Subtraction
The answer to an addition or subtraction calculation should be rounded to the same number of decimal places (not significant digits) as the measurement with the LEAST number of decimal places.

9. 12.52 m + 349.0 m + 8.24 m = 369.76 m2 Should be rounded to 369.8 m2
Examples:
12.52 m m m = m2
Should be rounded to m2
m – m = m2
Should be rounded to m2

10. Review
How many significant digits are in each of the measurements below:
1) 100 m _________ 2) m/s _______ ) m ________
4) 2.0 x 1011 m/s ______ 5) 50 metersticks _______ 6) s ________
Answer in the correct number of significant digits.
7) cm cm = _____________ or _____________
8) cm x 0.18 cm = ___________ or ____________
9) m2 ÷ m= ________________ or ___________
10) cm – cm = _______________ or _______________