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Hi, welcome to Math Antics.

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Now that you know all about fractions,

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from watching all of our fractions videos,

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it's time to learn about something called percentages.

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Percentages are super important.

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Have you ever been in a math class and heard another

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student as a teacher?

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Um, excuse me, a teacher?

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When are we ever going to use this stuff?

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You know, like, in real life?

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Well, when it comes to percentages,

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the answer is 100% of the time.

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Alright, maybe not 100% of the time, but a lot.

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Percentages are used every day to calculate things like how

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much sales tax you pay when you buy something,

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how much something costs when it's on sale,

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how much fiber is in your granola bar,

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or how much money you can make if you invest it in the

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stock market.

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That's all real life stuff for sure,

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so you can see that it's really important to understand

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percentages and how we use them in math.

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Alright then,

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are you ready to learn the key to understanding

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percentages, or percents as they're called for short?

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Drumroll please.

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A percent is a fraction.

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What?

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That's right, a percent is a fraction.

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And since you already know all about fractions,

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learning about percents is going to be easy.

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But a percent isn't just any old fraction.

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A percent is a special fraction that always has 100 as the

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bottom number.

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If it's a percent, then no matter what the top number is,

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the bottom number will be 100.

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In fact,

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because the bottom number of a percent is always 100,

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we don't even write it.

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Instead,

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we use this handy little symbol called a percent sign.

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Whenever you see this symbol after a number,

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it means the number is a percent.

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It's really a fraction with 100 on the bottom,

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but it's just being written in this more compact form.

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Like this number 15 here.

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It's got the percent sign after it,

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so we read it as 15 percent.

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And because a percent is really a fraction that always has

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100 as the bottom number,

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we know that it means the same thing as 15 over 100.

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Percents make even more sense if you know what the word

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percent means.

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The prefix of the word, per, means for each, or for every.

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You know, like if someone said, only one cookie per person,

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and the root word, cent, is Latin for 100.

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That's why there's 100 cents in a dollar.

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So percent literally means per 100,

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and that's why there are shortcuts for writing fractions

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that have 100 as the bottom number.

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Alright then, so whenever you see a percent like this,

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you know it can be replaced with,

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or converted to a fraction.

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Let's look at a few examples so you see the pattern.

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3% means 3 over 100.

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10% means 10 over 100.

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25% means 25 over 100. And 75% means 75 over 100.

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These are percents,

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and these are the fractions that they stand for.

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There's a few other interesting percents that we should

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take a look at, like this one.

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0%.

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Can you have 0 %?

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Yes, 0% would just mean 0 over 100.

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It's what we like to call a zero fraction,

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because its value is just zero.

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Remember, it's okay to have zero on the top of a fraction,

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but not the bottom.

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Alright then, what about 100%?

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Well, 100% just means 100 over 100.

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That's what we like to call a whole fraction.

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The top number is the same as the bottom,

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so its value is just one whole, or one.

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Okay then, 0% is just zero and 100% is just one,

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but what about numbers bigger than 100?

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Can you have 126%?

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Yup, it works exactly the same way.

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126% just means 126 over 100.

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And you know from the fractions videos,

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that's what we call an improper fraction.

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The top number is bigger than the bottom number,

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so the fractions value will be greater than 1.

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Alright team,

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I want you to go out there and give me 110% effort in

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today's game.

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But coach,

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it would be improper for us to give 110% effort in today's

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game!

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Okay, so now you know the key to percentages,

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that they're just special fractions that always have 100 as

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the bottom number.

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But there's one more thing that I need to tell you about in

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this video, and that's decimals.

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Do you remember in the video about fractions and decimals

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that you can convert any fraction into its decimal value?

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Sometimes it was kind of tricky converting to a decimal if

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we had to divide the top number by the bottom number.

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But other times, like when we had base 10 fractions,

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it was easy,

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because decimal number places are made for counting base 10

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fractions, like tenths, hundredths, and thousandths.

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Well guess what?

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Percents are base 10 fractions.

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They're hundredths because their bottom number is always

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100.

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That means it's really easy to rewrite a percentage as a

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decimal number.

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You can do it the same way as we did in the base 10

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fractions video.

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For example, we know that 15% is just 15 over 100, right?

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That's its fraction form.

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But it also has the decimal form 0.15 because this is the

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hundredths place and 0.15 means 15 hundredths.

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So, we can rewrite 15% as a fraction, 15 over 100,

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or as a decimal, 0.15.

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And now that you know why we can easily convert a

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percentage to a decimal,

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let me show you a really simple trick for doing it.

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First, you start with the number in percent form,

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like this, 35%.

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Next,

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you imagine where the decimal point should be in the number

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35.

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It's not shown, but if it was,

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it would be right here next to the ones place.

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Now remember, 35 and 35.0 are the same value.

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Now that you know where the decimal point is,

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just move it two number places to the left,

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away from the percent symbol, and draw it in right there.

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Last of all, once you've moved the decimal point,

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you erase the percent sign because you don't have a percent

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anymore.

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Moving the decimal point two places to the left converted

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it into the decimal value of that percent.

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Let's try converting a few more percents into their decimal

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values so you can get the hang of it.

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For 62%,

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we move the decimal point two places to the left and get 0

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.62.

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Remember,

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we can put an extra zero in front of the decimal point to

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be a placeholder and to make the decimal point easier to

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notice.

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For 75%, we move the decimal point and get 0.75.

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For 99%, we move the decimal point to get 0.99.

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Pretty cool, huh?

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Okay, but what about 4%?

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You might wonder how we can move the decimal point two

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places over when our number only has one digit.

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But all we need to do is use a zero as a placeholder in the

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number place that's missing.

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Then, when we move the decimal point two places over,

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we end up with a decimal value of 0.04.

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Now that makes sense because 4 is in the hundredths place

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and 4% is 4 over 100.

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And in the same way, 1% would just be 0.01.

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Again, we need that extra zero placeholder.

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Here's a few more interesting examples.

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0% would just be 0.00.

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And if we have 100% and we move the decimal point two

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places to the left, we end up with 1.00.

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But 1.00 is the same value as 1.

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And that's why 100% represents one whole.

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And if we have 142%,

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we move the decimal point to get 1 .42.

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That's a value greater than 1,

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which is what we would expect because 142% is really an

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improper fraction.

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142 over 100.

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Its value should be greater than 1.

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Alright,

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so now you know that a percent is a special fraction that

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always has 100 as the bottom number.

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And you know that you can rewrite percents in either their

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fraction form or their decimal form.

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25% is 25 over 100 or 0.25.

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But keep in mind that you could go the other way too.

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If someone gives you a fraction with 100 as the bottom

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number, you can rewrite it in percent form.

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If you get 12 over 100,

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you can say that's 12% and if you get 80 over 100,

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you can say that's 80%.

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Or, if you get the decimal, 0.10, you can say that's 10%.

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And if you get the decimal, 0.38, you can say that's 38%.

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So, that's the key to percentages.

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They're another way to write fractions in decimals,

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but there's a lot more to learn about how they're used in

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math,

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and we'll learn more about that in the next few videos.

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But for now,

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you should be sure that you really understand the basics of

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percentages by doing the exercises for this section.

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Thanks for watching Math Antics,

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and I'll see you next time.

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Learn more at www.mathantics .com