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Introduction to Percents

Introduction to Percents

Author: Sophia Tutorial

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

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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.

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.

? over 100

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.
25 % equals 25 over 100
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 % equals 3 over 100

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.

2 over 5 equals ? over 100
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.

fraction numerator 2 cross times 20 over denominator 5 cross times 20 end fraction equals 40 over 100
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%.

2 over 5 equals 40 over 100 equals 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.

2 over 3 equals 2 divided by 3 equals 0.6 with bar on top almost equal to 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%.

0.666 cross times 100 equals 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%.

66.6 % equals 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

A number that relates a part to the whole.