Three Ways to Show the Same Value

Fractions, decimals and percentages are all ways to describe parts of a whole. Being able to switch between them is one of the most useful maths skills you will learn.

Fraction	Decimal	Percentage
¼	0.25	25%
⅓	0.333...	33.3%
½	0.5	50%
¾	0.75	75%
1	1.0	100%

How to Convert

Fraction → Decimal

Divide the numerator by the denominator.

Example: ⅜ = 3 ÷ 8 = 0.375

Decimal → Percentage

Multiply by 100 (move decimal 2 places right).

Example: 0.375 × 100 = 37.5%

Percentage → Decimal

Divide by 100 (move decimal 2 places left).

Example: 45% ÷ 100 = 0.45

Decimal → Fraction

Write over the place value and simplify.

Example: 0.4 = 4/10 = 2/5

Fraction → Percentage Shortcut

If the denominator is a factor of 100, you can convert directly. Change the fraction so the denominator is 100 — the numerator becomes the percentage.

Example: Convert 7/20 to a percentage

Step 1: 20 × 5 = 100, so multiply top and bottom by 5.

Step 2: 7/20 = 35/100

Answer: 35%

Real-World Uses

Shopping Sales

A 25% off sale means you pay ¾ of the price. A $60 item costs $60 × 0.75 = $45.

Test Scores

You got 18 out of 20 on a test. That is 18/20 = 0.9 = 90%.

Key Vocabulary

Equivalent

Equal in value but written in a different form (e.g. ½ = 0.5 = 50%).

Percentage

A number expressed as a fraction of 100. The symbol % means "per hundred".

Numerator

The top number of a fraction. It tells you how many parts you have.

Denominator

The bottom number of a fraction. It tells you how many equal parts make the whole.

Worked Examples

1

Convert 3/5 to a decimal and a percentage.

Decimal: 3 ÷ 5 = 0.6

Percentage: 0.6 × 100 = 60%

2

Convert 0.15 to a fraction and a percentage.

Fraction: 0.15 = 15/100 = 3/20 (divide both by 5)

Percentage: 0.15 × 100 = 15%

3

A shop has a 20% off sale. A skateboard costs $85. What is the sale price?

Step 1: 20% as a decimal = 0.20

Step 2: Discount = $85 × 0.20 = $17

Step 3: Sale price = $85 - $17 = $68

Knowledge Check

Select the correct answer for each question. Click "Check Answer" to see if you are right.

Question 1

What is 3/4 as a percentage?

34% 80% 70% 75%

Question 2

Convert 0.35 to a fraction in its simplest form.

7/20 35/10 7/10 35/1000

Question 3

Which is the largest: 2/5, 0.45, or 35%?

2/5 0.45 35% They are all equal

Question 4

What is 60% as a fraction in its simplest form?

6/10 60/10 3/5 2/3

Question 5

A cricket team wins 7 out of 10 matches. What percentage of matches did they win?

7% 17% 700% 70%

Fractions, Decimals & Percentages