1. Dimensional Analysis The Factor-label Method of Conversions
Use Ratios with UNITS and Canceling

2. Conversion Factors: 1 dozen = 12 ; 5280 ft = 1 mile;
Problem: Use each of the following equivalencies (ratios) to determine how many inches are in 3 dozen miles.
Conversion Factors: 1 dozen = 12 ; 5280 ft = 1 mile;
12 inches = 1 foot.
Units match
3 doz.mi.
________________________________= in. 12
5280 ft
12 in
1 doz.
1 mi.
1 ft

3. 000,000,000,000, ,000,000,000,
P T G M k m μ n p
peta tera giga mega kilo milli micro nano pico

4. Convert 57 nm to mm. (n = 10-9, m = 10-3)
units match
57 nm
= mm
57 x 10-6
or: 5.7 x 10-5 mm
Got
Smaller
Got
Larger
Note the ratios used and how they were used:

5. Convert 93 km to nm. (n = 10-9, k = 103)
units match
93 km
= nm
93 x 1012
or: 9.3 x 1013 nm
Note the ratios used and how they were used:

6. Convert 68 μm to nm. (μ = 10-6, n = 10-9)
units match
68 μm
= nm
68 x 103
or: 6.8 x 104 nm