Often a quantity such a distance is given in one set of units when it would be better to have in a different set of units. In such cases it is important that you are able to convert such that the answer has the correct units.

For example, suppose you are driving a car at 30 mph for 15 minutes.
You can calculate the distance travelled from the formula distance = speed
x time, but are faced with the problem that the speed is measured in miles
per *hour*, whereas the time is measured in *minutes*. However,
if you remember that there are 60 minutes in an hour, you can convert the
time to be 0.25 hours, in which case the distance can be calculated as

Distance = 30 mph x 0.25 h = 7.5 miles.

In astronomy distances can be very large, and are often expressed in units which allow numerical values to be kept reasonably small, but which are unfamiliar to you. For example, the Andromeda galaxy is 2 million light years away. How far is that really? What is a light year? What is the distance in miles or in kilometers, units with which you are more familiar?

In trying to answer this question you need to know how to convert units
reliably, even when the quantities involved are outside your normal experience.
The method is based on that used in the simple example above. In converting
the time from minutes to hours you multiplied 15 minutes by a *conversion
factor* to get 0.25 hours. The trick is to make sure you get the conversion
factor the right way up.

Since we know from the conversion table that there are 93 million miles in one A.U. then the conversion from A.U. to miles is

Now that we have the answer in miles, we can use the conversion
factor that there are 6 trillion (6 x 10^{12}) miles in a light
year to convert this distance into light years

Note that the conversion could have been performed in two separate conversions, but can also be done using two multiplying factors in the one line, the first to make the required conversion metres to miles, and the other to convert seconds to hours.

The Andromeda Galaxy is 2 million light years away. If you have a spacecraft capable of travelling at one million miles an hour, how long would it take you to get there?

The calculation is a simple one, the time being calculated from the
formula **time = distance /speed**. Note that since the speed is quoted
in *miles* per hour, and the distance is in *light years*, one
will need to be converted. The answer will then be expressed in hours (since
that was the time unit in the speed) and should be converted to years to
give a true idea of just how long it takes.

More than a billion years. This gives us an idea of how vast the universe
is, and the immense times it takes to cover even a small portion of it.
The idea portrayed in science fiction programs such as Star Trek that inter-galactic
travel is possible within a one hour episode is not feasible. (You could
argue that with a faster speed you could travel the same distance in less
time, which is true. However, even with the best possible technology, you
can never hope to travel faster than the speed of light, and the journey
to the Andromeda Galaxy will take *at least* 2 million years.)