1. Applying Significant Figures
Conversions
Applying Significant Figures

2. Introduction
We often need to convert from one unit or set of units to another.
km → m
miles → m
mi/hr → m/s
gal → L
When we complete the conversion, we need to insure that we use the proper number of significant figures.

3. Introduction We can use a variety of different ways to do conversions.
All of these methods
rely on the same relationships
result in the same answer
have same limitations

4. Conversion Factors
The relationships we use to convert from one unit to another can be exact or approximate
Approximate relationships have a limited number of significant figures
1 qt. = 0.95 L = L
1 psi = atm = atm
Exact relationships have no effect on the number of significant figures
1 ft = 12 in

5. Conversions In order to convert from one unit to another unit
we analyze the problem to determine the conversion factors we need
we do a series of multiplications
to change our measurement from one unit
to the next unit
When we are finally at the desired unit - we are done.

6. Analysis During analysis, we write down the unit used for measurement
write down the unit we are looking for
write down the conversion factors to go from the measurement to the desired unit.
2.54 cm = 1 in cm
12 in = 1 ft mi
5,280 ft = 1 mi

7. Analysis Now we have conversion factors We turn them into fractions
We make sure the fractions have the units we are converting from on the bottom and the units we are converting to on the top
2.54 cm = 1 in
2.54 cm
1 in
12 in
1 ft
5,280 ft
1 mi cm
12 in = 1 ft mi
5,280 ft = 1 mi

8. Multiplication
Using the conversion factors we arrange our multiplication
For example: converting 500. cm to miles -
2.54 cm
1 in
12 in
1 ft
5,280 ft
1 mi
2.54 × 12 × 5,280
500. × 1 × 1 × 1 mi
500. cm × × × =
3.11 × 10-3 mi
2.54 cm
1 in
12 in
1 ft
5,280 ft
1 mi cm × × × = mi

9. Multiplication
An alternate method for arranging our conversion factors is using boxes
For example: converting 500. cm to miles -
500. cm 1
2.54 cm
1 in
12 in
1ft
5,280 ft
1 mi =
3.11 × 10-3 mi
2.54 cm
1 in
12 in
1 ft
5,280 ft
1 mi cm × × × = mi

10. Example Convert 6.50 cups of water to liters of water.
Set out the start and finish.
Set out the conversion factors (as fractions)
Set up the multiplication
6.50 c 1
1pt
1 c
1qt
2 pt L
1 qt = L
3.08 L
1 pt
2 c
1 qt
2 pt L
1 qt c L