Answer :
Final answer:
Dimensional analysis is used to convert between different units. Conversions for each blank are: a) ft = 12 in, b) m = 1,000,000,000 Mm, c) dL = 0.1 L, d) g = 1,000,000 ug, e) cm = 0.01 m, f) m = 0.001 km.
Explanation:
a) ft = ____ in In every foot, there are 12 inches. Therefore, for 1 foot, we have 1 ft = 12 in. b) m = ____ Mm A meter is a basic measure of length in the metric system. There are 1,000,000 (or 1x10^6) meters in a megameter. Since we're converting from meters to megameters, we divide 1 by 1,000,000 to get 0.000001 (or 1e-6) megameters. Therefore, 1 m = 1e-6 Mm. c) dL = ____ L A Deciliter is one-tenth of a liter.
Hence, 1 deciliter is equal to 0.1 liters. Therefore, 1 dL = 0.1 L. d) g = ____ ug The prefix 'micro' means 'one-millionth'. Hence, there are 1,000,000 micrograms in a gram. Hence, 1 gram is equal to 1,000,000 micrograms. So, 1 g = 1,000,000 ug. e) cm = ____ m A centimeter is one-hundredth of a meter. Hence, 1 centimeter is equal to 0.01 meters. Therefore, 1 cm = 0.01 m. f) m = ____ km A kilometer is 1,000 meters.
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