1. Aim: How do we convert between units with different metric prefixes?

2. Factor Label Method of Unit Conversion
Suppose we want to convert 53 g into kg. In order to do this, we must first find the factor label. The factor label is a ratio between two different units and is always equal to 1 In this case, there are two factor labels that we can use. (1 kg/ 1000 g or kg/1 g)

4. Example
To convert 53 g into kg, we multiply 53 g by the factor label 53g ( 1 kg/1000g)= kg Note: The gram unit cancels out leaving the kilograms.

6. Practice Problems Convert 345 cm into m Convert 65,000 g into kg
Convert 6.1 x 10-6 m into nm
Convert 9.31 x 102 Mg into g
Convert 132 s into cs
Convert 87.5 Tm into m
Convert 90,400 ps into s
Convert 12.5 cm into m

8. Measurement and Uncertainty-Significant Figures
The number of significant figures in a measurement can be used to express something about the uncertainty.
Rules for significant figures:
All nonzero numbers are significant figures.
All zeros between nonzero numbers are significant figures.
If the number is less than 1, all leading zeros are not significant zeros.
If the number is greater than 1 and there is no decimal present, all ending zeros are not significant figures.

9. Practice-Determine the number of significant figures in each quantity
How many significant figures?
53,000,000 eV m
4 x 10-4ns
78.9 g
2.46 x 10-6 pL Tm

10. Rules for adding-subtracting and multiplying-dividing measurements
When adding or subtracting, the number of decimal places in the result should equal the smallest number of decimal places of any term in the sum.
When multiplying (or dividing) quantities, the number of significant figures in the final answer is the same as the number of significant figures in the quantity having the lowest number of significant figures.

11. Practice Problems
How many significant figures are in the following numbers?
78.9m – 0.2m
s x 7 s
3.788 m x kg
1.85 cm – 0.2 cm