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# Introduction to Percents

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Author: Sophia Tutorial
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In this lesson, students will learn about percents as a part of a whole.

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Tutorial
This tutorial is an introduction to percents through the definition and discussion of:
1. What Is a Percent?
2. Percents As Fractions
3. Converting Fractions and Decimals to Percents

## 1. What Is a Percent?

A percent or percentage is a number that relates a part to the whole, where the whole is always 100. The word percent literally means “per 100.” 50%, then, means 50 per every 100. The symbol % means percent in the percentage form of a number.

Percentage
A number that relates a part to the whole

Percentages are used in daily life, like in the case of interest rates. An interest rate of 5% on a loan means that you paid five additional dollars for every \$100 you borrowed. Percentages are also used to report data.

If 60% of people own their own home in a certain community, this means that 60 out of every 100 people own their own home.

## 2. Percents as Fractions

You can think of percents as fractions as well. In the fraction form of a percent, 100 is the denominator.

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.
Or, suppose you 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.

## 3. Converting Fractions and Decimals to Percents

How can you determine the percentage equivalent of a fraction? There are two general methods for converting a percent into a fraction.

The first method is to write an equivalent fraction with a denominator of 100. You can do this because you know that a percentage can be thought of as a portion of 100 or a certain number per 100.

Suppose you want to convert the fraction 2/5 into a percentage. The first step is to write an equivalent fraction with 100 as the denominator.

If you want the 5 in the denominator to be converted to 100, you will need to multiply it by 20, because 5 times 20 equals 100. However, if you multiply the denominator by 20, you must also multiply the numerator by 20. Therefore, you now have 5 times 20 equals 100 in the denominator, and 2 times 20 equals 40 in the numerator.

Now you can see that 2/5 becomes 40 out of 100, or 40 per 100, which can also be expressed as 40%. When the denominator is 100, the numerator is your percent. Therefore, 2/5 is equal to 40%.

Not all fractions can be easily written with a denominator of 100, so there is a second method that will easily work for all fractions. In this method, you convert your fraction into a percent by first converting the fraction to a decimal, and then converting the decimal to a percent.

Suppose you want to convert the fraction 2/3 into a percent.
Step 1: You 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, you want to use 3 decimal digits, writing 0.6 repeating as 0.666.

Step 2: Now you want to convert your decimal to a percent form. To do this, you can multiply your decimal by 100 using your calculator. This can also be done without a calculator, because multiplying by 100 is the same as moving the decimal point two places to the right. In either case, you have 0.666 times 100 equals 66.6. Therefore, 2/3 is equal to approximately 66.6%.

Step 3: Lastly, you can round 66.6% to the nearest percent. Since the 6 after the decimal point is greater than 5, this means that you should round up, to 67%. 66.6%, then, is approximately equal to 67%.

Always make sure to include a percentage sign when writing numbers in percentage form.

Today you learned the definition of the word percent, which means ‘per 100’, and that you can write percents as a fractions, where the percent is the part and 100 is the whole. You also learned that you can convert a fraction to a percent by writing an equivalent fraction with a denominator of 100. Finally, you learned that you can 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.

Source: This work is adapted from Sophia author Colleen Atakpu.

Terms to Know
Percentage

A number that relates a part to the whole.