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Introduction to Percents

Introduction to Percents

Author: Colleen Atakpu

In this lesson, students will learn about percents as a part of a whole.

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[MUSIC PLAYING] Let's look at our objectives for today. We'll start by looking at, what is a percent? We'll then see how we can think of percents as fractions. We'll look at how to convert a fraction to a percent and finally, how to convert a decimal to a percent.

Let's look at what a percent actually is. A percent is a number that relates a part to the whole where the whole is always 100. The word percent literally means per 100. So for example, 50% means 50 per every 100. This symbol means percent in the percentage form of a number.

Percentages are used in daily life, for example, interest rates. An interest rate on a loan of 5% means you paid five additional dollars for every $100 you borrow. Percentages are also used to report data. For example, if 60% of people own their own home in a certain community, that means 60 out of every 100 people on their own home.

We can think of percents as fractions as well. In the fraction form of a percent, 100 is the denominator. So for example, if you have a coupon for 25% off, you would save $25 for every $100 you spend. 25% as a fraction would be 25 over 100, where 25 is the part and 100 is the whole. If we look at another example, suppose we have a certain country that has been able to reduce their environmental emissions by 3% over the last two years. 3% as a fraction would be 3 over 100, where 3 is the part and 100 is the whole.

So let's see how we can determine the percentage equivalent of a fraction. There are two general methods for converting a percent into a fraction. Our first method is to write an equivalent fraction with a denominator of 100. We do this because we know that a percentage can be thought of as a portion of 100 or how much you have per 100.

So let's look at converting the fraction 2/5 into a percentage. We want to write an equivalent fraction with 100 as the denominator. So we want to write 2/5 as something over 100. If we want the 5 in the denominator to be 100, we have to multiply by 20, because 5 times 20 would equal 100. But if we multiply by 20 and the denominator, we have to multiply by 20 in the numerator as well.

So we have 5 times 20 equals 100 in the denominator, and 2 times 20, which equals 40 in the numerator. So 2/5 becomes 40 out of 100, 40 per 100, or 40%. When the denominator is 100, the number in the numerator is our percent. So 2/5 is equal to 40%.

Not all fractions can be easily written with a denominator of 100. So now let's look at a second method that will easily work for all fractions. In this second form, we convert our fraction into a percent by first converting the fraction to a decimal and then the decimal to a percent.

Suppose we want to convert the fraction 2/3 into a percent. We can first convert 2/3 into a decimal using a calculator. The value of 2/3 is the same as 2 divided by 3. Typing this into the calculator reveals that 2/3 is equal to 0.6 repeating or 0.6 with a bar above the 6, meaning that the 6 keeps on repeating. In order to round to the nearest percent, we want to use 3 decimal digits so we can write 0.6 repeating as 0.666.

Next to convert from decimal to percent form, we can multiply by 100 using our calculator. But multiplying by 100 is the same as moving the decimal point two places to the right. In either case, we have 0.666 times 100 equals 66.6. Therefore, 2/3 is equal to approximately 66.6%. Rounding this to the nearest percent gives us 67% as the 6 after the decimal point is greater than 5, meaning we should round up. Always make sure to include a percentage sign when writing numbers in percentage form.

Let's look at our important points from today. Make sure you get them in your notes so you can refer to them later. The word percent means per 100. Percent can be written as a fraction, where the percent is the part and 100 is the whole.

We can write a fraction as a percent by writing an equivalent fraction with a denominator of 100. And we can also write a fraction as a percent by first converting the fraction to a decimal using division and then converting the decimal to a percent by multiplying by 100. So I hope that these key points and examples helped you understand a little bit more about percents. Keep using your notes, and keep on practicing. And soon, you'll be a pro. Thanks for watching.

Terms to Know

A number that relates a part to the whole.