Conversion Factors

There are twelve inches in a foot.

Therefore there are 24 inches (2 X 12) in two feet.

Someone who is six feet tall is 72 inches (6 X 12) tall.

The statement "1 foot = 12 inches" is an example of a conversion factor. It tells us how to change feet into inches. It can also be expressed as a fraction, like so:

12 inches / 1 foot

Read as "12 inches per one foot" or "12 inches in one foot."

Look carefully at the fraction above. since 12 inches and 1 foot are the same thing, this fraction is numerically equal to 1! This is what makes convrsion factors so useful; since they are effectively equal to one, we can multiply them by any number and not fundamentally change that number. It's the same as multiplying by 1!

Here's the procedure in a nutshell:

Identify the unit that you want the figure to have.

Identify the unit that the number has already that you want to get rid of.

Find a conversion factor (or a number of factors) that relate the unit you want to the unit you have.

Write out the fraction such that the unit you don't want is in the denominator, and the unit you do want is in the numerator.

Multiply your figure by this fraction.

Eliminate the unit you don't want. It should "cancel out."

Let's show how this is done. How many feet are in 3.5 miles?

We want units of feet

We want to eliminate units of miles.

The conversion factor is "1 mile = 5280 feet."

We write this as (5280 feet / 1 mile)

We multiply 3.5 miles X (5280 feet / 1 mile)

We have miles in the numerator and denominator, so they "cancel out," and we are left with feet:

3.5 ~~miles~~ X (5280 feet / 1 ~~mile~~) = 18,480 feet

Now use the fact that 1 minute = 60 seconds to find the number of seconds in 15 minutes. Check your answer on the next page.

Questions? Ask the designer, Jim Heath