# How do unit conversions work?

Jun 17, 2018

It involves simple algebra (multiplication or division) using conversion factor (numerical relationship between the two units).

#### Explanation:

Jun 17, 2018

Unit conversions use conversion factors to change the units of a measurement.

#### Explanation: For example, you buy a 1.7 kg smoked ham. How much is this in pounds?

You use a conversion factor to change the units.

What is a conversion factor?

A conversion factor is a multiplying fraction that is alway equal to one.

You use the conversion factor that relates grams and pounds.

You may know that

$\text{1 kg = 2.2 lb}$

(It's actually 2.204 62 kg, but we can use the approximate number here.)

If you divide both sides of the equation by 2.2 lb, we get

$\text{1 kg"/"2.2 lb" = "2.2 lb"/"2.2 lb} = 1$

If you divide both sides by 1 kg, we get

$\text{1 kg"/"1 kg" = "2.2 lb"/"1 kg} = 1$

Thus, the conversion factor can be either $\text{1 kg"/"2.2 lb}$ or $\text{2.2 lb"/"1 kg}$ because each equal to one.

How do I use a conversion factor for unit conversions?

$\text{1.7 kg = ? lb}$

Thus, the conversion factor is either

$\textcolor{b l u e}{\text{1 kg"/"2.2 lb}}$ or $\textcolor{b l u e}{\text{2.2 lb"/"1 kg}}$

You use the one with the desired unit ("lb") on top.

For this problem, you would write

1.7 color(red)(cancel(color(black)("kg"))) × color(blue)("2.2 lb")/(color(blue)(1) color(red)(cancel(color(blue)("kg")))) = "3.7 lb"

Notice that putting "kg" on the bottom makes the units cancel and gives an answer with the units of "lb".

If you had used the other conversion factor, you would have gotten

$\text{1.7 kg" × color(blue)("1 lb"/"2.2 kg") = "0.77 lb"^2"kg"^"-1}$

The units make no sense, so this choice is wrong.

Here's another way to think of using unit conversions.