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. \(\color{blue}{1.20 \text{ and } 1 \frac{1}{5}}\)

Frequently Asked Questions

How do you represent a percentage?

You can represent a percentage in three equivalent ways: as a percent, a fraction over 100, or a decimal. For example, 45% means 45 out of 100, so it can be written as 45/100, which simplifies to 9/20, or as the decimal 0.45. To go from percent to decimal, divide by 100; to go back, multiply by 100.

How do you represent percentage in a pie chart?

In a pie chart, each percentage becomes a slice of the full circle, and the whole circle stands for 100%. To draw a slice, multiply the percent by 360°. For example, 25% of 360° is 90°, a quarter of the circle, and 10% is 36°. Check that all the percentages add up to 100% before you draw.

How do you represent percentage in a bar graph?

In a percentage bar graph, the vertical axis is labeled from 0% to 100% (or to the highest value you need), and each bar’s height shows its percent. If 40% of a class chose soccer, the soccer bar reaches the 40% line. Label the axis with the % sign so readers know the bars show parts of 100, not counts.

How do you represent percentage change?

Percentage change is written as (new value − old value) ÷ old value × 100%. A positive result is an increase and a negative result is a decrease. For example, if a price goes from $40 to $50, the change is 10 ÷ 40 = 0.25, so it is a 25% increase. Always divide by the original amount, not the new one.

Can a percent represent a probability?

Yes. A probability is a number from 0 to 1, and you can show it as a percent from 0% to 100%. A probability of 0.3 is the same as a 30% chance, and a fair coin landing on heads has a probability of 1/2, or 50%. A percent above 100% cannot be a probability, because nothing is more than certain.

Can percentages be added or averaged?

Percentages can be added only when they are parts of the same whole, such as 30% and 45% of one class adding to 75% of that class. Averaging is trickier: if the groups are different sizes, a simple average of the percents is misleading. Instead, add up the actual parts, divide by the combined total, and 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