Fractions, Decimals and Percentages

Introduction

Fractions, decimals and percentages are three ways to write the same idea: parts of a whole. You meet them in discounts, recipes, tips, tax and test scores. Being able to switch between them is a very useful everyday skill.

The same number, three ways

A fraction shows parts of a whole: 3/8 means 3 parts out of 8.
A decimal writes the same value using place value: 0.375.
A percentage means "out of 100": 37.5%.

To convert:

Fraction to decimal: divide the top by the bottom. 3 divided by 8 is 0.375.
Decimal to percentage: multiply by 100. 0.375 x 100 = 37.5%.
Percentage to decimal: divide by 100. 37.5% = 0.375.
Percentage to fraction: write over 100 and simplify. 25% = 25/100 = 1/4.

Common values worth knowing:

Fraction	Decimal	Percentage
1/2	0.5	50%
1/4	0.25	25%
3/4	0.75	75%
1/5	0.2	20%
1/10	0.1	10%
1/3	0.333...	33.3%

Quick quiz

What is 3/8 as a percentage?

A percentage of an amount

"Per cent" means "per hundred." To find a percentage of an amount, convert the percentage to a decimal and multiply.

15% of 80: 0.15 x 80 = 12.
10% of any number: move the decimal point one place left. 10% of 80 is 8. Then 5% is half of that, 4. So 15% is 8 + 4 = 12. Mental maths shortcuts like this are handy for tips and discounts.

Percentage increase and decrease

To increase by a percentage, multiply by (1 + the decimal). To decrease, multiply by (1 minus the decimal).

Price 60 with 20% off: 60 x 0.8 = 48.
Price 60 with 20% added: 60 x 1.2 = 72.

A common trap

Increases and decreases of the same percentage do not cancel. Take 100, increase by 20 percent to 120, then decrease by 20 percent: 120 x 0.8 = 96, not 100. The second percentage applies to a different base, 120 and not 100.

To find the percentage change between two numbers: (new minus old) divided by old, times 100. From 50 to 65: (65 - 50) / 50 = 0.3, so 30 percent increase.

Be careful with percentage points. If an interest rate rises from 4 percent to 5 percent, that is a rise of 1 percentage point, but a 25 percent relative increase.

Try it yourself

Convert 7/20 to a decimal and a percentage. Find 35 percent of 240. Work out the price of an item costing 85 after 15 percent off. Check by estimating first.

Summary

Fractions, decimals and percentages are different ways to write parts of a whole.
Multiply by the decimal form to find a percentage of an amount, and by 1 plus or minus the decimal to increase or decrease.
Equal percentage rises and falls do not cancel, and percentage points differ from percent.