Representing Percentage

How to representing percentage, step by step: the rule in plain language, solved examples worked one line at a time, and practice questions so you can try it yourself before moving on.

A percentage is a way of expressing a number as a part of 100. The word “percent” literally means per hundred. Percentages are used everywhere, discounts, test scores, statistics, and nutrition labels. Learning to represent and interpret percentages is a core GED Math skill.

What Is a Percentage?

The symbol % means “out of 100.” So (color{blue}{45%}) means 45 out of every 100, which can also be written as the fraction (color{blue}{frac{45}{100}}) or the decimal (color{blue}{0.45}). Any percentage can be represented in three equivalent forms:

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• Percent: (color{blue}{45%})
• Fraction: (color{blue}{frac{45}{100} = frac{9}{20}})
• Decimal: (color{blue}{0.45})

How to Represent a Percentage

Converting a percent to a decimal

Divide the percent by 100 (move the decimal point two places to the left).

• (color{blue}{25% rightarrow 25 div 100 = 0.25})
• (color{blue}{8% rightarrow 0.08})
• (color{blue}{130% rightarrow 1.30})

Converting a percent to a fraction

Write the percent over 100, then simplify.

• (color{blue}{75% = frac{75}{100} = frac{3}{4}})
• (color{blue}{40% = frac{40}{100} = frac{2}{5}})

Converting a decimal or fraction to a percent

Multiply by 100 (move the decimal point two places to the right).

• (color{blue}{0.08 rightarrow 0.08 times 100 = 8%})
• (color{blue}{frac{3}{4} rightarrow 0.75 times 100 = 75%})

Step-by-Step Summary

1. To convert percent → decimal: divide by 100 (shift decimal 2 left).
2. To convert percent → fraction: write over 100, then simplify.
3. To convert decimal → percent: multiply by 100 (shift decimal 2 right).
4. To convert fraction → percent: divide numerator by denominator, then multiply by 100.

Watch: What Are Percentages? (Video Lesson)

Math Antics explains what percentages mean and how to represent them visually and numerically:

Worked Examples

Example 1: Represent 25% as a decimal and as a fraction in simplest form.

Decimal: (color{blue}{25 div 100 = 0.25}). Fraction: (color{blue}{frac{25}{100} = frac{1}{4}}).
Answer: 0.25 and (color{blue}{frac{1}{4}})

Example 2: Write (color{blue}{frac{3}{4}}) as a percent.

(color{blue}{3 div 4 = 0.75}). Multiply by 100: (color{blue}{0.75 times 100 = 75%}).
Answer: 75%

Example 3: Convert 0.08 to a percent.

(color{blue}{0.08 times 100 = 8%}).
Answer: 8%

Example 4: A class has 30 students. 18 passed the quiz. What percent passed?

(color{blue}{frac{18}{30} = 0.60 times 100 = 60%}).
Answer: 60%

More Practice: Finding a Percent of a Number

Math with Mr. J shows how to apply percentages to numbers, a natural next step after learning to represent them:

Exercises

1. Write 60% as a decimal and as a fraction in simplest form.
2. Convert 0.035 to a percent.
3. Write (color{blue}{frac{7}{20}}) as a percent.
4. A bag contains 50 marbles. 35 are red. What percent are red?
5. Express 120% as a decimal and as a mixed number.

Answers

1. (color{blue}{0.60 text{ and } frac{3}{5}})
2. (color{blue}{3.5%})
3. (color{blue}{35%})
4. (color{blue}{70%})
5. (color{blue}{1.20 text{ and } 1 frac{1}{5}})

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Frequently Asked Questions

Can a percent be greater than 100?

Yes. A percent greater than 100 means the quantity exceeds the whole. For example, (color{blue}{150%}) means one and a half times the original amount. As a decimal it is (color{blue}{1.50}).

What does 0% mean?

(color{blue}{0%}) means none of the whole, zero out of 100. As a decimal it is (color{blue}{0}), and as a fraction it is (color{blue}{frac{0}{100} = 0}).

How do I quickly convert a fraction to a percent?

If the denominator divides evenly into 100, scale the fraction: multiply numerator and denominator by (color{blue}{100 div text{ denominator }}). Otherwise, divide numerator by denominator to get the decimal, then multiply by 100.

Related Topics

• Using Decimals, Grid Models and Fractions to Represent Percent
• Word Problems Involving Percentage of a Number
• Solving Percentage Word Problems
• Fractional and Decimal Percentages
• Convert Between Fractions and Decimals