Math Antics - What Are Percentages?

Summary

The Math Antics video script introduces percentages as special fractions with 100 as the denominator, simplifying their representation with a percent sign. It explains how percentages are ubiquitous in daily life, from sales tax to stock market returns. The script teaches that percentages can be easily converted to decimals by moving the decimal point two places to the left, and vice versa, highlighting their practicality and connection to real-world applications. Viewers are encouraged to practice with exercises to solidify their understanding of this fundamental math concept.

Takeaways

• 📚 Percentages are fractions with a denominator of 100, represented by the percent sign (%).
• 🛒 They are used in everyday life for calculating sales tax, discounts, nutritional content, and investment returns.
• 🔢 The term 'percent' comes from 'per centum' in Latin, meaning 'per hundred', which is why the bottom number is always 100.
• 👍 Understanding percentages is crucial for real-life applications and is built upon the knowledge of fractions.
• 📉 Zero percent (0%) is equivalent to the fraction 0/100, representing a value of zero.
• 💯 One hundred percent (100%) is equivalent to the fraction 100/100, which simplifies to 1, representing a whole.
• 🔑 Any percentage can be converted to a fraction by placing the percentage number over 100.
• 🔄 Percentages can also be converted to decimals by moving the decimal point two places to the left and removing the percent sign.
• 📈 Improper fractions, where the numerator is greater than the denominator, can be represented as percentages greater than 100.
• 📝 The script encourages practicing the conversion of percentages to fractions and decimals through exercises.
• 📺 The video is part of a series on Math Antics, which aims to explain mathematical concepts in an engaging way.

Q & A

What is the main topic of the Math Antics video?

The main topic of the video is percentages, explaining what they are, how they are used, and their relationship with fractions and decimals.

Why are percentages considered important in real life?

Percentages are important in real life because they are used daily to calculate sales tax, discounts on sales, nutritional content, and investment returns, among other things.

What is the relationship between a percent and a fraction?

A percent is a special type of fraction where the denominator is always 100. It represents a part of a whole divided into 100 equal parts.

How is the percent sign (%) used in representing percentages?

The percent sign is used after a number to indicate that the number is a percentage. It is a shorthand way of writing a fraction with 100 as the denominator.

What does the word 'percent' literally mean?

The word 'percent' comes from the Latin word 'per centum', which means 'per 100'. It indicates a ratio or fraction with 100 as the denominator.

Can you provide an example of how to convert a percentage to a fraction?

Yes, for example, 15% can be converted to a fraction as 15/100, which simplifies to 3/20.

What is the decimal equivalent of 100%?

The decimal equivalent of 100% is 1.00, which represents a whole or a complete value.

How can you convert a percentage to a decimal?

To convert a percentage to a decimal, you move the decimal point two places to the left and remove the percent sign. For example, 35% becomes 0.35.

What is the significance of 0% in terms of fractions?

0% is equivalent to 0/100, which is considered a 'zero fraction' because its value is zero.

Can percentages be greater than 100%, and if so, what does that represent?

Yes, percentages can be greater than 100%. For example, 126% means 126/100, which is an improper fraction where the numerator is greater than the denominator, indicating a value greater than one.

How can you convert a decimal to a percentage?

To convert a decimal to a percentage, you move the decimal point two places to the right and add the percent sign. For example, 0.25 becomes 25%.

Outlines

00:00

📊 Introduction to Percentages

This paragraph introduces the concept of percentages as a fundamental part of mathematics with real-life applications. It explains that percentages are a type of fraction with 100 as the denominator, represented by the percent sign (%). The paragraph uses everyday examples such as sales tax, discounts, nutritional content, and stock market returns to illustrate the importance of percentages. It also clarifies that a percent is a fraction with 100 as the bottom number, which can be read as 'X percent' and is equivalent to the fraction X/100. The significance of the word 'percent' is also discussed, with 'per' meaning 'for each' and 'cent' being Latin for 100, hence 'per 100'. Examples are given to show how different percentages can be represented as fractions (e.g., 3% as 3/100) and how special cases like 0% and 100% are treated as zero and one whole, respectively. The concept of improper fractions is also briefly touched upon with the example of 126%.

05:03

🔢 Converting Percentages to Decimals

This paragraph focuses on converting percentages to decimals, a process that's straightforward due to percentages being base-10 fractions. It outlines a simple trick for this conversion: starting with the percentage number, visualizing the decimal point two places to the left of the number, moving the decimal point two places to the left of the number, and then erasing the percent sign. Examples are provided to demonstrate this method, showing how percentages like 62%, 75%, and 99% are converted to 0.62, 0.75, and 0.99, respectively. The paragraph also addresses how to handle single-digit percentages by using a zero as a placeholder, as seen with 4% becoming 0.04. Additional examples include 0% equating to 0.00 and 100% to 1.00, reinforcing that 100% represents a whole. The paragraph concludes by emphasizing that percentages can be rewritten in fraction or decimal form, and that understanding this conversion is key to mastering the basics of percentages.

Keywords

💡Percentages

Percentages are a way to express a number as a fraction of 100. They are fundamental to the video's theme, as they are introduced as a real-life application of math. In the script, percentages are used to illustrate concepts such as sales tax, discounts, nutritional content, and investment returns, showing their ubiquity in everyday life.

💡Fractions

Fractions are a mathematical representation of parts of a whole, where a numerator represents the part and the denominator represents the total number of equal parts. The video explains that percentages are a type of fraction with a denominator of 100, which simplifies the representation and understanding of parts of a whole.

💡Percent Sign (%)

The percent sign is a symbol used to denote that a number is a percentage. In the script, it is highlighted as a shorthand way to represent fractions with a denominator of 100, making it easier to read and understand the proportion of a whole that the number represents.

💡Sales Tax

Sales tax is a percentage of the price of商品 or services that is added to the final price. The video uses sales tax as an example of how percentages are used in financial calculations, emphasizing the practical application of percentages in everyday transactions.

💡Discount

A discount is a reduction in the price of an item, typically expressed as a percentage of the original price. The video script mentions discounts to demonstrate how percentages can be used to calculate the new price of an item after a reduction.

💡Fiber

Fiber refers to the indigestible parts of plant foods that are important for health. In the context of the video, fiber content in a granola bar is given as a percentage, showing how percentages are used to communicate nutritional information.

💡Stock Market

The stock market is a platform where shares of publicly traded companies are bought and sold. The video mentions the stock market to illustrate how percentages can represent potential gains or losses on investments, tying into the financial aspect of percentages.

💡Zero Fraction

A zero fraction is a fraction where the numerator is zero, resulting in a value of zero. In the script, 0% is described as a zero fraction, which is 0 over 100, emphasizing that even zero can be represented as a percentage.

💡Whole Fraction

A whole fraction is a fraction where the numerator and denominator are equal, resulting in a value of one. The video uses 100% as an example of a whole fraction, which is 100 over 100, to show that percentages can represent a complete or whole value.

💡Improper Fraction

An improper fraction is a fraction where the numerator is greater than the denominator, resulting in a value greater than one. The video explains that percentages over 100, like 126%, are improper fractions, indicating a value that exceeds the whole.

💡Decimal

A decimal is a way of representing fractions with a denominator of 10, 100, 1000, etc., using a decimal point. The video teaches that percentages can be easily converted to decimals by moving the decimal point two places to the left, showing the connection between percentages and base-10 fractions.

Highlights

Percentages are a fundamental concept in mathematics with real-life applications.

Percentages are used to calculate sales tax, discounts, nutritional content, and investment returns.

A percent is essentially a fraction with 100 as the denominator.

The percent sign (%) is a shorthand for fractions with 100 in the denominator.

The term 'percent' derives from 'per 100', highlighting its relationship with fractions.

Examples are given to show how percentages are represented as fractions (e.g., 3% is 3/100).

0% is equivalent to a zero fraction, and 100% is a whole fraction, equal to 1.

Percentages greater than 100, like 126%, are improper fractions with values greater than 1.

Decimals can be easily converted from percentages due to their base-10 nature.

A simple trick is demonstrated for converting percentages to decimals by moving the decimal point two places to the left.

Conversion examples are provided to illustrate the process (e.g., 62% becomes 0.62).

Special cases like 4% are explained, using a zero as a placeholder for decimal conversion.

The video clarifies that 100% as a decimal is 1.00, representing a whole.

Percentages can also be converted from decimals by moving the decimal point two places to the right and adding a percent sign.

The video emphasizes the importance of understanding the basics of percentages through exercises.

The video concludes by encouraging viewers to learn more about percentages in upcoming videos.

Transcripts

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