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

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 2280960 1 doz. 1 mi. 1 ft

000,000,000,000,000.000,000,000,000, 1015 1012 109 106 103 10-3 10-6 10-9 10-12 P T G M k m μ n p peta tera giga mega kilo milli micro nano pico

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:

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:

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