dimensional analysis?

Question

Im having trouble trying to attempt this conversion problem:
Given: 1km=.62 mile
speed of light=3.0x10^8 m/s
Convert: 89 x 10^6 miles to minutes to the correct amount of significant digits

Answer 1

For conversion problems, you are simply multiplying by "1" repeatedly.

For example, to convert 8 miles/hour into meters/second:

(8 mile / hour) * (1 hour / 60 minute) * (1 minute / 60 seconds) * (5280 feet / 1 mile) * (12 inches / 1 foot) * (2.54 cm / inch) * (1 meter / 100 cm)

Each term after the (8 mile/hour) is equal to 1. You just flip each term so that the units cancel in the way you'd like. If you have "miles" in the numerator, multiply by a term that has miles in the denominator, and the unit you'd like in the numerator. Likewise, if you have "hours" in the denominator, multiply by a term that has hours in the numerator, and the unit you'd like in the denominator.

Answer 2

89x10^6 miles / 0.62 miles/km = 143.5x10^6 km
143.5x10^6 km x 1000 m/km = 143.5x10^9 m
143.5x10^9 m / 3.0x10^8 m/s = 47.8x10^1 s
47.8x10^1 s / 60 s/min = 8.0 minutes