Dimensional analyst on my chemistry homework?

Question

light travels at a speed of 186 000 miles/second. How many kilometers will it travel in exactly four hours? ( 1 km = 0.621 mile)

Answer 1

Here's how to do this:

1. We first convert hours to seconds. There are 3600 seconds in 1 hour.

There are two ways in writing this conversion factor:

1 hour / 3600 s    and     3600 s / 1 h

We have to choose which way we should write out this conversion factor in such a way that the known unit (given, that is h) cancels out. The desired unit should be left out uncanceled.

In this case, we choose choice B because in this way, the h cancels out and we end up with s (desired unit, unknown).

4 h * 3600 s / 1 h

2. Since we now know how many seconds there are in an hour, we can now proceed into knowing how many kilometers are there in a mile.

We have the given that light travels at a speed of 186 000 miles/s. Again, we need to decide as to how we could write out this given in such a way that the known unit (this time, it's s) cancels out. We need to leave the unit miles uncanceled.

In here, we put miles on top and seconds below so that the seconds will cancel out.

4 h * 3600 s / 1 h * 186 000 miles / 1 s

4. Since we now know how many miles light can travel in 4 hours, we will now determine how many kilometers light will travel.

Recall that 1 km = 0.621 mile

We have to put km on top and miles at the bottom so that the miles will cancel out and kilometers will be left uncanceled.

4 h * 3600 s / 1 h * 186 000 miles / 1 s * 1 km / 0.621 mile

= 4.31 * 10^9 km

:)