Percentages

What are Percentages?

A percentage is a way of expressing a number as a fraction of 100. The word "percent" means "per hundred" and is represented by the symbol %.

25% = 25/100 = 0.25

25% means 25 out of 100, or 25 per hundred.

Percentages are used to express parts of a whole, comparisons, changes, and many other relationships.

Converting Between Percentages, Decimals, and Fractions

Percentage to Decimal

To convert a percentage to a decimal, divide by 100 (or move the decimal point two places to the left).

75% = 75 ÷ 100 = 0.75

8% = 8 ÷ 100 = 0.08

125% = 125 ÷ 100 = 1.25

0.5% = 0.5 ÷ 100 = 0.005

250% = 250 ÷ 100 = 2.5

33.3% = 33.3 ÷ 100 = 0.333

Decimal to Percentage

To convert a decimal to a percentage, multiply by 100 (or move the decimal point two places to the right).

0.45 = 0.45 × 100 = 45%

0.07 = 0.07 × 100 = 7%

1.5 = 1.5 × 100 = 150%

0.005 = 0.005 × 100 = 0.5%

2.25 = 2.25 × 100 = 225%

0.333 = 0.333 × 100 = 33.3%

Percentage to Fraction

To convert a percentage to a fraction, write it over 100 and simplify if possible.

25% = 25/100 = 1/4

75% = 75/100 = 3/4

20% = 20/100 = 1/5

50% = 50/100 = 1/2

40% = 40/100 = 2/5

12.5% = 12.5/100 = 1/8

Fraction to Percentage

To convert a fraction to a percentage, divide the numerator by the denominator and multiply by 100.

1/4 = 0.25 × 100 = 25%

3/5 = 0.6 × 100 = 60%

7/8 = 0.875 × 100 = 87.5%

2/3 = 0.667 × 100 = 66.7%

1/3 = 0.333 × 100 = 33.3%

3/4 = 0.75 × 100 = 75%

Percentage Calculations

Finding a Percentage of a Number

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

What is 25% of 80?

25% = 0.25

0.25 × 80 = 20

Therefore, 25% of 80 is 20.

Finding What Percentage One Number is of Another

To find what percentage one number is of another, divide the first number by the second and multiply by 100.

What percentage of 80 is 20?

20 ÷ 80 = 0.25

0.25 × 100 = 25%

Therefore, 20 is 25% of 80.

Finding the Original Number Given a Percentage

To find the original number when you know a percentage of it, divide the part by the percentage (as a decimal).

20 is 25% of what number?

25% = 0.25

20 ÷ 0.25 = 80

Therefore, 20 is 25% of 80.

Percentage Increase and Decrease

Percentage Increase

To find the percentage increase, divide the amount of increase by the original amount and multiply by 100.

A price increases from $80 to $100. What is the percentage increase?

Amount of increase = $100 - $80 = $20

Percentage increase = (20 ÷ 80) × 100 = 25%

Percentage Decrease

To find the percentage decrease, divide the amount of decrease by the original amount and multiply by 100.

A price decreases from $80 to $60. What is the percentage decrease?

Amount of decrease = $80 - $60 = $20

Percentage decrease = (20 ÷ 80) × 100 = 25%

Finding the Final Amount After a Percentage Change

To find the final amount after a percentage increase or decrease, you can use a multiplier.

For a 25% increase: Multiply by 1.25 (1 + 0.25)

$80 × 1.25 = $100

For a 25% decrease: Multiply by 0.75 (1 - 0.25)

$80 × 0.75 = $60

Practice Percentages

Test your knowledge with our interactive percentage practice exercises.

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Percentage Calculator

Use our calculator to solve percentage problems quickly and easily.

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Real-World Applications

1
Discounts and sales (20% off the original price)
2
Tax calculations (8% sales tax added to purchases)
3
Tips at restaurants (15-20% of the bill)
4
Interest rates on loans and savings accounts
5
Statistics and data analysis (percentage of survey respondents)

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