**Introduction**

In this lesson, you will learn how to convert from one unit to another using what are called unit conversions (simple equations to help you change from unit to unit). Unit conversions is just a matter of taking the measurement of something in one set of units and changing it to an equivalent measurement but in a different set of units. This lesson covers the conversion of hours (hr) and minutes (min) as well as inches (in) and centimeters (cm).

This video illustrates the lesson material below. Watching the video is optional.

**Unit Conversions**

A unit conversion is taking the measurement of something in one set of units and changing it to an equivalent measurement in another set of units.

**Example 1**

A rectangle includes six, equally sized boxes, three in the top row, and three in the bottom row. Each box represents an inch. The base of the rectangle is three inches. What is that length in centimeters?

Figure 1

The calculation to do this is a unit conversion because you are converting from inches to an equivalent length in centimeters.

\begin{align*} inches \rightarrow centimeters \end{align*}

The key to unit conversions is the concept that:

- anything divided by itself is equal to one such as \(\large\frac{x}{x} = 1\), and
- one multiplied by anything is equal to itself as well \(1x =x\).

Fractions used in unit conversions are called conversion factors. A conversion factor is a key that shows something in the numerator and denominator that are equal to each other. For example:

\begin{align*} 1 \;inch &= 2.54\; centimeters &\color{red}\small\text{Unit equivalents}\\\\ &\frac{1\;inch}{2.54\;centimeters} &\color{red}\small\text{Conversion factor}\\\\ &\frac{2.54\;centimeters}{1\;inch} &\color{red}\small\text{Conversion factor} \end{align*}

Both fractions are equal to one. They don’t look the same, but they represent the same length. They both represent the same conversion factor.

Take what you know and multiply it by the conversion factor. Remember that the conversion factor has an interchangeable numerator and denominator, meaning that you can put either number in the top or bottom and it will not change the conversion factor. Here you put inches in the denominator because you are trying to convert to centimeters.

\begin{align*} &\frac{3in}{1}\times \frac{2.54cm}{1in} &\color{red}\small\text{Multiply by the conversion factor} \end{align*}

The units that are the same in opposite positions (numerator and denominator), will cancel out.

\begin{align*} &\frac {3 \color{red}\cancel{in}}{1} \times \frac{2.54cm}{1 \color{red}\cancel{in}} &\color{red}\small\text{Inches cancel out} \end{align*}

In this case, the inches cancel out. You are left with \(3\times2.54cm\) over 1.

\begin{align*} &\frac{3 \times 2.54cm}{1} = 7.62cm &\color{red}\small\text{Simplify the fraction} \end{align*}

After simplifying, you are left with 7.62cm. Therefore,

\begin{align*} 3in &= 7.62cm\\ &or \\

7.62cm &= 3in \end{align*}

**Example 2**

How many hours is 14 minutes?

\begin{align*}14\; minutes = ?\; hours \end{align*}

Note this conversion factor:

\begin{align*} 60 \;minutes&= 1\; hour&\color{red}\small\text{Unit equivalents}\\\\ &\frac{1\;hour}{60\;minutes}&\color{red}\small\text{Conversion factor}\\\\ &\frac{60\;minutes}{1\;hour}&\color{red}\small\text{Conversion factor}\\\\ \end{align*}

Both fractions are equal to one. They don’t look the same, but they represent the same length of time. They both represent the same conversion factor.

Now, multiply what you know by the conversion factor.

\begin{align*} &\frac{14\;min}{1}\times \frac{1\;hr}{60\;min} &\color{red}\small\text{Multiply by the conversion factor}\\\\ & \frac {14 \color{red}\cancel{min}}{1} \times \frac{1hr}{60 \color{red}\cancel{min}} &\color{red}\small\text{Minutes cancel out}\\\\

&\frac{14 hr}{60} &\color{red}\small\text{Multiply fractions across}\\\\

& 0.23hr &\color{red}\small\text{Simplify the fraction} \end{align*}

14 minutes is 0.23 hours.

In review, start with what you know and determine what you want in the end. Next, find a conversion factor that changes the units. Multiply what you know by the conversion factor in such a way that the undesired units cancel each other out. Simplify the fraction as needed.

**Things to Remember**

- Start with what you know and determine what you want in the end.
- Anything divided by itself always equals one.
- Units that are opposite (top to bottom) cancel each other out.
- The numerator and denominator of a conversion factor are interchangeable.

### Practice Problems

equal to approximately \(4.23\) cups. Convert the amount of water in Margaret’s pitcher to cups. Round to the nearest hundredth. (

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