At times, you will need to convert units. Some conversion factors you know, such as 60 seconds in a minute, 12 inches in a foot, etc. Others, such as the number of seconds in a year, require a bit of calculation.

Keep in mind that if you do not use consistent units, troubles will arise. NASA dramatically illustrated the cost of such errors when it lost a spacecraft in 1999. A company supplied data to NASA based on British units (pounds) when NASA engineers expected metric units (newtons). Oops. That, alas, was the end of that space probe (and about $125 million and, one suspects, some engineer’s NASA career).

As NASA’s misfortune indicates, you need to make sure you use the correct units when solving physics problems. If a problem presents information about a quantity like time in different units, you need to convert that information to the same units.

You convert units by:

1. Knowing the conversion factor (say, 12 inches to a foot; 2.54 centimeters to an inch; $125 million to a spacecraft).
2. Multiplying by the conversion factor (such as 3.28 feet/1.00 meter) so that you cancel units in both the numerator and denominator. For example, to convert meters to feet, you multiply by 3.28 ft/m so that the meter units cancel. This may be easier to understand by viewing the example on the right.

In conversions, it is easy to make mistakes so it is good to check your work. To make sure you are applying conversions correctly, make sure the appropriate units cancel. To do this, you note the units associated with each value and each conversion factor.

As is shown on the right, a unit that is in both a denominator and a numerator cancels. You should look to see that the units that remain “uncancelled” are the ones that you desired. For instance, in the example problem, fluid ounces cancel out, and the desired units, milliliters, remain.