Math Antics – What Are Percentages?

Hi! Welcome to Math Antics. Now that you know all about fractions, from watching all of our fractions videos, it’s time to learn about something called “percentages”. Percentages are super important. Have you ever been in a math class and heard another student ask the teacher: Um.. excuse me… teacher… Ah… when are we ever gonna use this stuff? Ya know… like in real life? Well when it comes to percentages, the answer is one-hundred percent of the time. Well alright… maybe not a hundred percent of the time… but a lot! Percentages are used every day to calculate things like: …how much sales tax you pay when you buy something. …how much something costs when it’s on sale. …how much fiber is in your granola bar. …or how much money you can make if you invest it in the stock market. That’s all real life stuff for sure. So, you can see that it’s really important to understand percentages and how we use them in math. Alright then… are you ready to learn the key to understanding percentages, or percents as they’re called for short? Drum roll please… A percent is a fraction! Whaaaat? That’s right… a percent IS a fraction! And since you already know all about fractions, learning about percents is gonna be easy. But a percent isn’t just any old fraction. A percent is a special fraction that always has 100 as the bottom number. If it’s a percent, then no matter what the top number is, the bottom number will be 100. In fact, because the bottom number of a percent is always 100, we don’t even write it. Instead, we use this handy little symbol (%) called a percent sign. Whenever you see this symbol after a number, it means the number is a percent. It’s really a fraction with 100 on the bottom, but it’s just being written in this more compact form. …like this number 15 here. It’s got the percent sign after it, so we read it as “15 percent”, and because a percent is really a fraction that always has 100 as the bottom number, we know that it means the same thing as 15 over 100. Percents make even more sense if you know what the word precent means. The prefix of the word (per) means “for each” or “for every”. Ya know like if someone said, “only one cookie per person”. And the root word (cent) is Latin for 100. That’s why there’s 100 cents in a dollar. So, percent literally means “per 100” and that’s why they’re shortcuts for writing fractions that have 100 as the bottom number. Alright then, so whenever you see a percent like this, you know it can be replaced with (or converted) to a fraction. Let’s look at a few examples so you see the pattern. 3% means 3 over 100 10% means 10 over 100 25% means 25 over 100 and 75% means 75 over 100 These are percents… and these are the fractions that they stand for. There’s a few other interesting percents that we should take a look at. …like this one: 0% …can you have 0% ? Yes! 0% would just mean 0 over 100. It’s what we like to call a “zero fraction” cuz its value is just zero. Remember, it’s okay to have zero on the top of a fraction, but not the bottom! Alright then, what about 100%. Well 100% just means 100 over 100. That’s what we like to call a “whole fraction”. The top number is the same as the bottom, so its value is just one whole, or 1. Okay then, 0% is just zero, and 100% is just 1. But what about numbers bigger than 100? Can you have 126% ? Yep, it works exactly the same way. 126% just means 126 over 100. And you know from the fractions videos, that’s what we call an “improper fraction”. The top number is bigger than the bottom number, so the fraction’s value will be greater than 1. Alright team, I want you to go out there and give me a-hundred and TEN percent effort in today’s game! But coach… it would be “improper” for us to give a-hundred and ten percent effort in today’s game. Okay, so now you know the key to percentages. …that they’re just special fractions that always have 100 as the bottom number. But there’s one more thing that I need to tell you about in this video, and that’s decimals. Do you remember in the video about fractions and decimals that you can convert any fraction into its decimal value? Sometimes it was kind of tricky converting to a decimal if we had to divide the top number by the bottom number. But other times, like when we had “base-10” fractions, it was easy because decimal number places are made for counting base-10 fractions, (like tenths, hundredths and thousandths). Well guess what… Percents ARE base-10 fractions! They are hundredths because their bottom number is always 100. That means it’s really easy to re-write a percentage as a decimal number. You can do it the same way as we did in the base-10 fractions video. For example, we know that 15% is just 15 over 100, right? That’s its fraction form. But it also has the decimal form 0.15 because THIS is the hundredths place and 0.15 means 15 hundredths. So, we can re-write 15% as a fraction (15 over 100) OR as a decimal (0.15) And now that you know WHY we can easily convert a percentage to a decimal, let me show you a really simple trick for doing it. First, you start with the number in percent form like this: 35% Next, you imagine where the decimal point should be in the number 35. It’s not shown, but if it was, it would be right here next to the ones place. (Now remember, 35 and 35.0 are the same value.) Now that you know where the decimal point is, just move it two number places to the left (away from the percent symbol) and draw it in right there. Last of all, once you have moved the decimal point, you erase the percent sign because you don’t have a percent anymore. Moving the decimal point two places to the left converted it into the decimal value of that percent. Let’s try converting a few more percents into their decimal values so you can get the hang of it. For 62 percent, we move the decimal point two places to the left and get 0.62 (Remember, we can put an extra zero in front of the decimal point to be a place holder and to make the decimal point easier to notice.) For 75 percent, we move the decimal point and get 0.75 For 99 percent, we move the decimal point to get 0.99 Pretty Cool, huh? Okay, but what about 4% ? You might wonder how we can move the decimal point two places over when our number only has one digit. But all we need to do is use a zero as a place holder in the number place that’s missing. Then, when we move the decimal point two places over, we end up with the decimal value of 0.04. Now that makes sense because 4 is in the hundredths place and 4% is 4 over 100. And in the same way, 1% would just be 0.01. Again, we need that extra zero placeholder. Here’s a few more interesting examples: 0% would be just 0.00 And if we have 100% and we move the decimal point two places to the left, we end up with 1.00 But 1.00 is the same value as 1. That’s why 100% represent one whole. And if we have 142%, we move the decimal point to get 1.42 That’s a value greater than one which is what we’d expect because 142% is really an improper fraction (142 over 100) Its value should be greater than 1. Alright, so now you know that a percent is a special fraction that always has 100 as the bottom number. And you know that you can re-write percents in either their fraction form OR their decimal form. 25% is 25 over 100 or 0.25 But keep in mind that you could go the other way too. If someone gives you a fraction with 100 as the bottom number, you can re-write it in percent form. If you get 12 over 100, you can say that’s 12% And if you get 80 over 100, you can say that’s 80% OR… If you get the decimal 0.10, you can say that’s 10% and if you get the decimal 0.38, you can say that’s 38% So, that’s the key to percentages. They’re another way to write fractions and decimals. But there’s a lot more to learn about how they‘re used in math, and we’ll learn more about that in the next few videos. But for now, you should be sure that you really understand the basics of percentages by doing the exercises for this section. Thanks for watching Math Antics, and I’ll see ya next time! Learn more at www.mathantics.com