Units Dimensions and Conversions

One light-year is the distance that light travels in exactly one year.
If the speed of light is 6.7 x 10⁸ mph, convert light-years to:
a. miles
b. meters

(a) 5.9x10¹² mi   (b) 9.4x10¹⁵ m

Solution Steps:

We need to change 6.7x10⁸ miles in one hour to ?? miles in one year and then to ?? meters in one year. We'll need some conversion equations:

1 mi = 1.61x10³m

1 day = 24 hr

1 yr = 365 days

Notice that the last two equations can be combined to give:

1 yr = 8760 hr

Here are the two calculations:

We'll state the answers to two sig figs, since the speed of light was given that way.

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