# 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"?

Jan 25, 2017

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

$\text{1 kg}$ is literally larger than $\boldsymbol{\text{1 g}}$ by a factor of $\boldsymbol{1000}$. To make the fraction equal to $1$ then, we say that $\text{1 kg}$ $=$ $\text{1000 g}$ so that the number physically represents the same quantity in real life.

So, the conversion factor is:

$\boldsymbol{\text{1 kg"/"1000 g}}$

So, to convert $\text{1.023 g}$ to $\text{kg}$, you should recognize that the number will become smaller because a $\text{kg}$ is larger than a $\text{g}$ by a factor of $1000$.

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

or

$= \textcolor{b l u e}{1.023 \times {10}^{- 3}}$ $\textcolor{b l u e}{\text{kg}}$

An incorrect result would be $1.023 \times {10}^{3} = \text{1023 kg}$, 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.