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

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.,*

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.

### Examples

#### Example 1

20 m/s = ? mi/hr

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

0.0125 mi/s (60 s/min) = .75 mi/min

0.75 mi/min (60 min/hr) = 45 mi/hr

### Interactive Simulation

### Review

- Estimate or measure your height.
- Convert your height from feet and inches to meters.
- Convert your height from feet and inches to centimeters
(100cm=1m)

- 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
(ms)

- Convert the French speed limit of
140km/hr intomi/hr . - Estimate or measure your weight.
- Convert your weight in pounds into a mass in
kg - Convert your mass from
kg intoμg - Convert your weight into Newtons

- Convert your weight in pounds into a mass in
- Find the
SI unit for pressure. - An English lord says he weighs
12 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
10mi/hr every 2 seconds, how manymi/hr is the speed increasing every second? State your answer with the unitsmi/hr/s .

**Review (Answers)**

- a. A person of height
5ft .11in . is1.80m tall b. The same person is180cm - a.
3seconds=1/1200hours b.3x103ms 87.5mi/hr - If the person weighs
150lb then a. 67.9 kg (on Earth) b. 67.9 billionμg c. this is equivalent to668N - Pascals (Pa), which equals
N/m2 - a.
168lb .,b.76.2kg 5mi/hr/s