Students will learn how to convert units from metric to english system and vice verse using dimensional analysis.

### Key Equations

Guidance

- The key to converting units is to multiply by a clever factor of one. You can always multiply by 1, because it does not change the number. Since 1 in. is equal to 2.54 cm, then . Thus, one can multiply by this form of 1 in order to cancel units (see video below).
- Write out every step and show all your units cancelling as you go.
- When converting speeds from metric to American units, remember the following rule of thumb: a speed measured in mi/hr is about double the value measured in m/s (
*i.e.,*is equal to about 20 MPH). Remember that the speed itself hasn’t changed, just our representation of the speed in a certain set of units. - When you’re not sure how to approach a problem, you can often get insight by considering how to obtain the units of the desired result by combining the units of the given variables. For instance, if you are given a distance (in meters) and a time (in hours), the only way to obtain units of speed (meters/hour) is to divide the distance by the time. This is a simple example of a method called
*dimensional analysis*, which can be used to find equations that govern various physical situations without any knowledge of the phenomena themselves.

#### Example 1

**Question**: 20 m/s = ? mi/hr

**Solution**:

20 m/s (1 mi/1600 m) = .0125 mi/s

.0125 mi/s (60 s/min) = .75 mi/min

.75 mi/min (60 min/hr) = 45 mi/hr

### Watch this Explanation

### Time for Practice

- Estimate or measure your height.
- Convert your height from feet and inches to meters.
- Convert your height from feet and inches to centimeters

- Estimate or measure the amount of time that passes between breaths when you are sitting at rest.
- Convert the time from seconds into hours
- Convert the time from seconds into milliseconds

- Convert the French speed limit of into .
- Estimate or measure your weight.
- Convert your weight in pounds into a mass in
- Convert your mass from into
- Convert your weight into Newtons

- Find the unit for pressure.
- An English lord says he weighs stone.
- Convert his weight into pounds (you may have to do some research online)
- Convert his weight in stones into a mass in kilograms

- If the speed of your car increases by every 2 seconds, how many is the speed increasing every second? State your answer with the units .

**Answers**

- a. A person of height . . is tall b. The same person is
- a. b.
- If the person weighs then a. 67.9 kg (on Earth) b. 67.9 billion c. this is equivalent to
- Pascals (Pa), which equals
- a. .,b.