Question

What do you call a fraction that equals 1 that allows you to change from one unit to another? How do you construct one to go from `"1.023 g"` into `"kg"`?

Answer 1

This would be called a conversion factor. It's a fraction that equals `1`, but changes your units.

`"1 kg"` is literally larger than `bb"1 g"` by a factor of `bb1000`. To make the fraction equal to `1` then, we say that `"1 kg"` `=` `"1000 g"` so that the number physically represents the same quantity in real life.

So, the conversion factor is:

`bb("1 kg"/"1000 g")`

So, to convert `"1.023 g"` to `"kg"`, you should recognize that the number will become smaller because a `"kg"` is larger than a `"g"` by a factor of `1000`.

`1.023 cancel"g" xx "1 kg"/(1000 cancel"g") = color(blue)("0.001023 kg")`

or

`= color(blue)(1.023 xx 10^(-3))` `color(blue)("kg")`

An incorrect result would be `1.023 xx 10^(3) = "1023 kg"`, as you would have generated a mass that is `1000` times greater than the original quantity, when conversion factors should actually preserve the physical quantity.