Question

How many grams are in 74.0 mg?

Answer 1

`"mg"` stands for milligram.

• `"m"` is the prefix "milli", which means `10^(-3)`, a number less than `1`.
• `"1 mg"` is therefore literally smaller than `"1 g"`.

So, there are `10^(-3)` `"g"` in `"1 mg"`, or `10^3` `"mg"` in `"1 g"`. This makes sense because you need more of something small to equal something larger.

Due to the equivalences given above, we can use one of them as a conversion factor.

`74.0 cancel("mg") xx "1 g"/(10^3 cancel("mg"))`

`= 74.0 cancel("mg") xx (10^(-3) "g")/(1 cancel("mg"))`

`=` `color(blue)("0.074 g")`

You don't have to do it both ways, but both are provided so you can choose.