Percentages

A percentage is a way of expressing a number as a fraction of 100. The word comes from the Latin per centum, meaning “by the hundred.”

$\text{Percent} = \frac{\text{Part}}{\text{Whole}} \times 100$

Finding a Percent of a Number

To find a percent of a number, convert the percentage to a decimal and multiply.

Formula:

$\text{Result} = \text{Number} \times \frac{\text{Percent}}{100}$

Example 1: What is 25% of 80?

$80 \times \frac{25}{100} = 80 \times 0.25 = 20$

Answer: 25% of 80 is 20.

Example 2: What is 15% of 200?

$200 \times \frac{15}{100} = 200 \times 0.15 = 30$

Answer: 15% of 200 is 30.

Real-World Application: Nursing

A nurse needs to administer 20% of a 500 mL IV bag over the first hour.

$500 \times \frac{20}{100} = 500 \times 0.20 = 100 \text{ mL}$

The nurse should administer 100 mL in the first hour.

Finding What Percent One Number Is of Another

Formula:

$\text{Percent} = \frac{\text{Part}}{\text{Whole}} \times 100$

Example 3: 15 is what percent of 60?

$\frac{15}{60} \times 100 = 0.25 \times 100 = 25\%$

Answer: 15 is 25% of 60.

Real-World Application: Electrician

An electrician measures a 7.2-volt drop on a 240-volt circuit. What percent voltage drop is this?

$\frac{7.2}{240} \times 100 = 3\%$

Since the National Electrical Code recommends keeping voltage drop under 3%, this circuit is right at the limit.

Percent Change

Percent change tells you how much something increased or decreased relative to the original value.

Formula:

$\text{Percent Change} = \frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \times 100$

A positive result means an increase. A negative result means a decrease.

Example 4: A product’s price goes from $40 to$52. What is the percent change?

$\frac{52 - 40}{40} \times 100 = \frac{12}{40} \times 100 = 30\%$

Answer: The price increased by 30%.

Example 5: Your electric bill drops from $120 to$96. What is the percent change?

$\frac{96 - 120}{120} \times 100 = \frac{-24}{120} \times 100 = -20\%$

Answer: Your bill decreased by 20%.

Converting Between Percentages, Decimals, and Fractions

To convert a percentage to a decimal:

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

$45\% = \frac{45}{100} = 0.45$

To convert a decimal to a percentage:

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

$0.72 = 0.72 \times 100 = 72\%$

To convert a fraction to a percentage:

Divide the numerator by the denominator, then multiply by 100.

$\frac{3}{8} = 3 \div 8 = 0.375 = 37.5\%$

Practice Problems

Test your understanding with these problems. Click to reveal each answer.

Key Takeaways

• Percent of a number: multiply the number by the percent divided by 100
• What percent: divide the part by the whole, then multiply by 100
• Percent change: divide the difference by the original, then multiply by 100
• Converting between forms: percentages, decimals, and fractions all represent the same value in different ways

Next, learn about Arithmetic fundamentals, or try the Percentage Calculator to check your work.