Dimensional Analysis question
A very large unit of measurement is the zettameter (zm). 1 zm = 1021 m, but astronomers measures distances in even bigger units called astronomical units (the au). One au is defined to be approximately 107 miles (the average distance between the center of the earth and the center of the sun). An even bigger unit is called the parsec, which is equal to about 2x105 au. When astronomers talk about intergalactic space however it’s even more convenient to use units of kiloparsecs. Given that 1.6 km = 1 mile, about how many kiloparsecs are there in a zettameter?
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Yes, the work I've came up with so far is,
10^18 km x (1mi/1.6 km) x (1au/10^7 mi ) x )1 Kiloparsec/2x10^8 au)