Roots and Powers of Algebraic Expressions

Percents: Definition, Application & Examples

Maybe you know that 95% is an A and 75% is a C. But what do those percents really mean? In this lesson, we'll learn about percents, inclpercent-–-definitionuding how to convert them to fractions and decimals.

Percent – Definition

OK, team, I need you to give all you've got. I want you to go out there and give 110%. I know it sounds impossible. And, well, it is. Before we work on plays, let's talk about percents.

The word percent literally means 'per hundred.' We use this symbol - % - for percents.

Let's take the word apart. It's per and cent. Where have you seen 'cent' before? Well, it's the word for a penny. It's also in the word century. What's a century? A hundred years. And then there's centennial; that's the 100-year anniversary. A centipede has 100 legs. Well, I think it does. I've never tried to count. And a woman who has centuplets is going to be crazy tired.

Let's talk about what percents mean. When you're hitting 99% of your shots, what did you do? If you took 100 shots, you made 99 of them. 99 per one hundred, per-cent. But what if you took 1,000 shots? Whoa. I bet your arms are tired. 99% means that you got 99 out of each hundred. So 99% of 1,000 is 990. Hitting 99% of your shots would also make you the best basketball player in the history of the world.

Fractions & Decimals

This is a stats-driven game, so let's talk about what we can do with percents. We can convert percents to fractions quite easily. For example, our team makes 43% of its free throws. Let's say we want to convert 43% to a fraction. That's 43 per one hundred. As a fraction, it's 43/100. That's it!

And then there's Fred the Flying Monkey, our team mascot. He jumps off a trampoline to make crazy dunks during halftime. He only makes 8% of his dunks. That sounds bad, but it's actually one of the best percentages among flying monkeys, with or without trampolines.

Anyway, if we had 8%, it'd be 8/100. No matter what your percent, just put it over 100, and you've made it into a fraction. With 8/100, we can simplify that to 2/25, which still doesn't sound great.

What about decimals? What is 43% as a decimal? Just drop the percent sign and move the decimal two places to the left. So 43% becomes .43. Why? Because .43 is 43 one-hundredths.

I said we make 43% of our free throws. What if we wanted to know what 43% of 17 is. We had 17 free throws in the last game. If we multiply 17 times .43, we get 7.31. The team made 8 of 17 free throws, so we were slightly above our average percentage.

What about 8%? I know, I know. Fred doesn't like to talk about it. But still, just drop the sign and move the decimal two places to the left. So 8% becomes .08. The math is the same. To figure out his success in 50 attempts, we'd multiply 50 times .08, which is 4. Hey, 4 is better than 0!

Practice Problems

Let's try some practice problems involving percents. Just as there are different ways to win a basketball game, there are different ways to solve a percent problem. As we go through these, let's try a few different methods for solving them.

At a home game, 84% of the seats are filled. If there are 5,200 seats, how many seats are filled? To solve this, let's set up two fractions: 84/100 = x/5,200. Remember, 84% as a fraction is just 84/100. If we cross multiply, we get 100x = 436,800. Divide by 100, and we find out that 4,368 fans showed up.

We also could have converted 84% to a decimal. 84% would become .84. And then we just multiply .84 times 5,200, which is, again, 4,368.

Here's another one: If a team has 15 players and 9 travel for a road game, how many players stay home? This one has a little trick to it. Note that the question is asking how many players stay home. So instead of 9, we want 15 - 9, or 6. So what is 6 of 15?

If we set this up as a fraction, we have x/100 = 6/15. Cross multiply to get 15x = 600. 600 divided by 15 is 40. So 40/100 students stayed home. What is 40/100 as a percent? 40%. The bigger question is this: Where's the dedication on that team? 40% stayed home? Not cool.

Here's another one: In a game, a team makes 36 shots and misses 42. What percent of shots were made? The trick here is that we're not given the total. The fraction for the made shots isn't 36/42. It's 36/(36 + 42), so a total of 78 shots were attempted. To solve this one, let's try something different. Let's just divide 36 by 78. That gets us a decimal, .46. We can convert that to a percent by moving the decimal two places to the right. So .46 is 46%. The team made 46% of its shots.

Lesson Summary

To summarize, we learned about percents. 'Percent' means per hundred.

To convert a percent to a fraction, we just put the number over 100. 75% becomes 75/100. 2% becomes 2/100.

To convert a percent to a decimal, we drop the sign and move the decimal two places to the left. 15% becomes .15. 9% becomes .09.

Oh, and 110%? If 100% is the maximum you can give, how do you give 110%? Well, see, it's a metaphor. But that's a whole other topic...