Physics Help >> Index to Physics Homework Help » Converting Units

Using Conversion Factors

Converting units is like riding a bicycle: once you know how it’s easy. One method is to multiply the given unit by a conversion factor that cancels the unwanted unit and replaces it with the desired unit.

For example, to convert 2 hours to minutes you intuitively multiply by 60. But why does that work?

You see that h is in both the numerator and the denominator, so the h cancels, leaving you with minutes. (Related term: dimensional analysis.)

A common problem is how to convert grams to kilograms. For example, how many kg is 250 g?

250 g x (1 kg)/(1000 g) = 0.25 kg

Converting km/h to m/s

If you have two units at a time, you use two conversion factors. For example, to convert 50 km/h to m/s you convert km to m and 1/ h to 1/ s:

Converting three units at a time, requires you use three conversion factors. For example, to convert 50 mi/h to m/s you convert mi to km, km to m and 1/ h to 1/ s:

Converting mph to m/s

To convert miles per hour to m/s, we recall that there are 1.61 km in a mile, 1000 m in a km, and 3600 seconds in an hour:

60.6 mph * (1.61 km/mi)(1000m/km)(1h/3600s) = 60.6 * (.447) =27.1 m/s

Metric Conversions

Another method works well for converting between metric units. For example, the axon of a neuron has a diameter of 0.20 microns. Express this diameter in terms of nanometers.

(1 micron = 1 micrometer).

(Related search term: metric multipliers, SI multipliers, metric prefix.)

Problems

1.

a. A building is 555 ft high. Express this height in meters.
b. A man is 7 ft tall. What is his height in meters?

2. A filament has a diameter of 0.20 microns. Express this diameter in terms of a centimeter. (1 micron = 1 micrometer).

3. Change the following to the SI unit and in standard form:

a. 2.31 MJ

b. 1.5 gcm^-3

4. Convert 10 km/hr/s to m/s².

Answers

For solutions to all the problems on this page click here.

4.

(10 km/h/s)*(1000 m / km)*(3600 s / h) = 2.78 m/s/s = 2.78 m/s²