Games
Problems
Go Pro!

Converting Units with Exponents

Reference > Science > Unit Conversions
 

We've now covered almost everything you need to know in order to be an expert unit-converter. But there's one more scenario we should talk about: what happens if your units have exponents?

"What? Units can have exponents?" 

Sure! Units of area are things like ft2 and in2. Volume uses cubes (meter3), and when you deal with physics, you'll get some really scary units like kilogram x meter/second2!

Don't panic, though; it's really not all that difficult...

Example One - Convert 12 ft2 to inches2.

We start off as we normally do, by multiplying by our conversion factor (12 inches)/(1 foot):

(12 ft2) x (12 inches)/(1 foot) = 144 foot x inches.

You see what happened? One of the feet in feet2canceled, leaving us with a unit of foot x inch.

WHAT? That's a ridiculous looking unit - who ever heard of a foot-inch? What went wrong? Nothing went wrong. We just need to multiply our conversion factor TWICE:

(144 foot x inches) x (12 inches)/(1 foot) = 1728 inches2

If a unit has an exponent of 2, you need to daisy chain the conversion factor twice to get rid of the unit!

In fact, we can generalize that: If a unit has an exponent of n, we need to daisy chain the conversion factor n times to get rid of the unit.

Example Two - Convert 81 feet3 to yards3

Answer - Our conversion factor is (1 yard)/(3 feet), and we need to daisy chain it 3 times. But daisy chaining the conversion factor 3 times is the same as cubing it, right? So let's cube that conversion factor: 

(13 yard3)/(33 feet3) = (1 yard3)/(27 feet3).

Now let's use that conversion factor:

(81 feet3) x (1 yard3)/(27 feet3) = 3 yard3.
 

Questions

1.
What is the square of the conversion factor (12 inches)/(1 foot)?
2.
What is the cube of the conversion factor (7 days)/(1 week)?
3.
Convert 1 cubic yard to cubic feet.
4.
Convert 72 square inches to square feet.
5.
Convert 1,440,000 seconds2 to hours2.
6.
Convert 50 ft/s2 to miles/min2
Assign this reference page
Click here to assign this reference page to your students.
Converting Fractional UnitsConverting Fractional Units
Unit IndexUnit Index
 

Understanding Coronavirus Spread

A Question and Answer session with Professor Puzzler about the math behind infection spread.

Blogs on This Site

Reviews and book lists - books we love!
The site administrator fields questions from visitors.
Like us on Facebook to get updates about new resources
Home
Pro Membership
About
Privacy