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10 Metric Conversions and Unit Analysis Very small pm picometer x 103 ηm nanometer x 103 μm micrometer mm millimeter x 103 x 103 meter x 103 km kilometer x 103 Mm megameter x 103 Gm gegameter x 103 Tm terameter m Very big You should also know millimeter x 101 cm centimeter x 102 m meter mm We are going to use unit analysis to do some metric conversions. The main purpose of this is to learn unit analysis and secondly learn about metric conversions. To facilitate this you are only allowed to convert by 103 x per conversion. Please do the same in your workbook. We use unit analysis as our main calculation tool in Chemistry 11 and Chemistry 12. Learn it well and you will do awesome in chemistry. 1. Convert 1.23 x 1012 Mm to m- you can only convert by 103 in any one step! 1.23 x 1012 Mm x = 1 x 103 km x 1 Mm 1 x 103 m 1 km 1.23 x 1018 m Write the starting number and units Multiply with 1 Mm on the bottom and 103 km on top Mutiply with 1 km on the bottom and 103 m on top Do the math and round off to three sig figs 2. Convert 6.5 x 10-6 m to nm- you can only convert by 103 in any one step! 6.5 x 10-6 m = x 1 x 103 mm x 1 x 103 μm x 1 x 103 nm 1m 1 mm 1 μm 6.5 x 103 nm 3. Convert 6.5 x 106 nm to m- you can only convert by 103 in any one step! 6.5 x 106 nm = x 1 μm 1 x 103 nm 6.5 x 10-3 m x 1 mm x 1 x 103 μm 1m 1 x 103 mm 4. Convert 5.88 x 108 μm to km 5.88 x 108 μm x 1 mm x 1 m x 1 x 103 μm 1 x 103 mm = 5.88 x 10-1 km 1 km 1 x 103 m 5. Convert 65 m2 to mm2 65 m2 = x ( 1 x 103 )2 mm 2 2 1m 6.5 x 107 mm2 6. Convert 875 mm3 to m3 875 mm3 x = 8.75 x 10-7 m3 1 m3 ( 1 x 103 )3 mm 3