The Importance of Units and Percents

This is Day 7 of 31 Days of Math Learning Success. Follow all the days here and check out others that are writing for 31 days here.

” .002 dollars and .002 cents… they’re both the same if you, if you look at ’em on paper-wise”
~ Verizon Customer Service

It’s about 7 to my house from yours.

And it’s roughly 85 from your house to my weird Uncle Zeno’s house.

I hear you already, “Okay, Bon, you’ve lost it. It’s about 7 WHATs to my house?”

Exactly.

What’s in a unit?

Anything we measure requires a unit. That’s the “what” that things are measured in.

We can measure length in miles, kilometers, inches or even “Bon’s Right Big Toe.” But we have to measure in something. Otherwise you get insanity.

We measure area in square stuff – square inches, square meters or square big toes. (Okay that last one is a little weird. But it would work if you did it right.)

And you can also measure area in acres or hectares – which are square things to begin with.

Going over to volume (3D junk), we measure in cubic stuff like cubic inches or cubic feet.

But also we can measure in liters or gallons – which are cubic by their definitions.

There are secret units, too!

We don’t think of percentages as units, but they are.

A unit is an amount that can be used to determine the amounts of other things of the same kind.

Percentages are the generic unit.

If we want to measure the amount of male population of a country, we can say there are 151.8 million males in the U.S. And there are 31 million males in the U.K.

But that doesn’t give us the “same kind” of measurement of males.

Sure there are more males in the U.S. – there’s a whole lot more space for them. But how does that allow us to compare?

Instead, we can say 49.2% of the U.S. population is male, while 49.05% of the U.K. population is male.

Pretty even when you look at it that way.

But for China, there are 696.3 million males – 52% of the population.

And for some more dramatic ends of the spectrum, the Ukraine has 46% males and the U.A.E. has 69%.

Now we can start comparing!

Be careful mixing percents AND units!

Here’s where things can get really sideways.

Consider 25 cents (USD). That’s 25% of one dollar. Those are the same values but one is in units and one is in percents AND units.

Now what is 25% of one cent?

Yipes!

Check out a visual on it:

25% of a dollar vs. 25% of a cent

Here are some equivalent ways of writing each

25% of a dollar
One U.S. quarter
$0.25
25 cents
25¢
1/4 of a dollar

25% of a cent
$0.0025
Not even one cent!
0.25¢
Pretty stinkin’ useless to bother about

Confused yet?

Probably not. Because we’ve gone through it slowly. And compared it gently.

But it can get weird.

If you want to see just how weird, listen to this recording of George Vaccaro struggling with his Verizon bill. He was quoted “.002 cents per kilobyte,” and then charged .002 dollars per kilobyte: