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# How to Use Percentages to Easily Calculate Tips Learn how to use the power of ten percent, and not your calculator, to easily and quickly calculate how much to tip.

By
Jason Marshall, PhD
Episode #12

## How to Use Percentages to Easily Calculate Tips

A few articles ago, I asked if you ever found yourself at restaurants fumbling to figure out how much to tip; I guessed that you might occasionally resort to seeking advice from your “smart” phone; and I told you that you really didn’t need to. But I didn’t tell you why you didn’t need to because we first needed to cover some basics about fractions. And now that we’ve done that, it’s time to go back and talk about the power of ten percent—soon to be known as: the reason you’ll abandon your favorite tip-calculating iPhone app forever. And it doesn't stop here, because next week I'll show you how to use percentages to easily calculate sales prices in your head.

## What Are Percentages?

Let’s start by figuring out what percentages actually are and where they come from. It might not be obvious, but fractions and percentages are inextricably linked. In fact, percentages are fractions! But they’re not just any old type of fraction—percentages are special: they’re fractions where the denominator (the bottom part) always has a value of 100. And since this denominator is always the same, it doesn’t need to be written down. That’s why percentages only have one number instead of two like normal fractions.

## What Does “Percent” Mean?

Now, let’s take a closer look to see where this all comes from. What does “percent” actually mean? Well, let’s split it into two words and see if the meaning becomes clearer: percent = “per cent.” That is the same “cent” as in the word “century,” which means 100 years. So “per cent” means “per 100,” or “for each 100.” What does something like 1 percent—or 1%—actually mean then? Well, 1% literally means 1 per 100. Or, in fractional lingo: one one-hundredth—1/100. ## How to Use Money to Understand Percentages

Here’s an easy way to think about percentages: The US dollar (and many other currencies around the world) is broken up into 100 parts—called cents! (The use of the word “cent” here is no coincidence.) So, you can think of percentages as portions of \$1. For example: What’s 1% of \$1? Well, since 1% means 1/100 of something, and 1 cent is 1/100 of \$1, 1% of \$1 must be 1 cent. Okay, how about 10% of \$1. Well, if 1% of \$1 is 1 cent, then 10% of \$1 must be 10 times that. Which, of course, is 10 cents—also known as a dime.

Okay, so 10% means 10/100 in fractional terms, but we also just said that 10% of \$1 is a dime. But a dime, being worth 10 cents, is 1/10 of a dollar. So, the fraction 10/100 must be equivalent to 1/10! This isn’t surprising if you’re familiar with “reducing fractions to lowest terms”—a topic which we’ll talk about in the future. But, for now, the important thing to remember is that 10% and 1/10 are the same fraction. Why is that important?

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