The following video will show how to do unit conversions and explains why it works.

Video Source (11:42 mins) | Transcript

**Introduction to Unit Conversions**

Unit conversion = taking the measurement of something in one set of units and changing it to an equivalent measurement in another set of units.

The keys to doing unit conversions are the concepts that anything divided by itself is equal to 1 and that anything multiplied by 1 is equal to itself.

\( {\dfrac {x}{x}} = 1 \)

and

\( 1x = x \)

**Conversion Factors**

Conversion factors are fractions where the item in the numerator is equal to the item in the denominator, essentially making the fraction equal to 1.

Examples:

1 inch = 2.54 cm, therefore:

\( {\dfrac {1 \ inch}{2.54 \ cm}} = 1 \)

This is the conversion factor between inches and centimeters.

Another example is that 60 minutes = 1 hour, therefore:

\( {\dfrac {60 \ minutes}{1 \ hour}} = 1 \)

This is the conversion factor between minutes and hours.

**Example 1: Inches to Centimeters**

How do we convert 3 inches into the equivalent length in centimeters?

- Start with what we know: 3 inches.
- Determine what we want to get in the end: centimeters.
- Determine the conversion factor to use: 1 inch = 2.54 cm.
- Multiply by 1 in the form of the conversion factor that cancels out the unwanted units. In this case, \( {\frac {2.54 \ cm}{1 \ in}} \).

\( \dfrac{\color{DarkGreen}3 {\cancel{\text{ inches}}}}{1}\left ( \dfrac{{\color{DarkOrange} 2.54\:\text{cm}}}{{\color{DarkGreen} 1\:\cancel{\text{ inch}} }} \right ) = \dfrac{\left ( {\color{DarkGreen} 3} \right )\left ( {\color{DarkOrange} 2.54\:\text{cm}}\right )}{1} = {\color{Black} 7.62\:\text{cm}} \)

Answer: 3 in = 7.62 cm

**Example 2: Minutes to Hours**

How do we convert 14 minutes into the equivalent time in hours?

\( 14 \ minutes = ? \ hours \)

- Start with what we know: 14 minutes.
- Determine what we want to get in the end: hours.
- Determine the conversion factor to use: 60 minutes = 1 hour.
- Multiply by 1 in the form of the conversion factor that cancels out the unwanted units. In this case, \( {\frac {1 \ hour}{60 \ minutes}} \).

\({14\color{Magenta}\cancel{\text{ minutes}}}\times \dfrac{{1\color{green} \text{ hour}}}{{60\color{Magenta} \cancel{\text{ minutes}}}}=\dfrac{(14\times 1){\color{green} \text{hours}}}{60} \)

\(=0.23{\color{green}\text{ hours}} \)

Answer: **14 minutes = 0.23 hours**

## Additional Resources

- Khan Academy: Converting Units: U.S. Volume (5:16 mins; Transcript)
- Khan Academy: Converting Units: Metric Distance (4:01 mins; Transcript)
- Khan Academy: Same Length in Different Units (5:47 mins; Transcript)

### Practice Problems

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