Understanding Dimensional Analysis: Converting Units with Factor-Label Method
This resource explores the Factor-Label Method of dimensional analysis, focusing on converting units through ratio relationships. By applying equivalencies such as 1 dozen = 12, 5280 feet = 1 mile, and 12 inches = 1 foot, we can derive conversions like how many inches are in 3 dozen miles. Additionally, it covers conversions involving nanometers (nm) to millimeters (mm), kilometers (km) to nanometers, and micrometers (μm) to nanometers. Understanding how to manipulate these ratios is essential for accurate unit conversions in scientific contexts.
Understanding Dimensional Analysis: Converting Units with Factor-Label Method
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Presentation Transcript
Dimensional Analysis The Factor-label Method of Conversions Use Ratios with UNITS and Canceling
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. 12 5280 ft 12 in ________________________________= in. 2280960 1 doz. 1 mi. 1 ft
000,000,000,000,000.000,000,000,000, 1015101210910610310-310-610-910-12 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 57 x 10-6 = mm or: 5.7 x 10-5 mm Got Larger Got Smaller Note the ratios used and how they were used:
Convert 93 km to nm. (n = 10-9, k = 103) units match 93 km 93 x 1012 = nm 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 68 x 103 = nm or: 6.8 x 104 nm
