Question

what conversion factor should be used to convert from meters to gigameters

Answer 1

\[10^{9}\]
http://en.wikipedia.org/wiki/Gigametre

Answer 2

^pretty much

Answer 3

\( 10^9 \ \text{meters} = 1 \ \text{gigameter} \)

Our goal is to convert [from meters] [to gigameters].
Say we were given \(x\) meters.
\( x \ \text{meters} \)
To get rid of the units of meters, we divide off the meters. Then we multiply by gigameters.
\( x \ \cancel{\text{meters}} \times \dfrac{1 \ \text{gigameter}}{10^9 \ \cancel{ \text{meters}}} \)
\( = \ x \times 10^{-9} \ \text{gigameters} \)
So our conversion factor is the 1 gigameter / (10^9 meters).
Notice that multiplying by 1 gigameter and then dividing by 10^9 meters is the equivalent of multiplying by 1, thus not changing the value, because 10^9 meters is the same as 1 gigameter.