Converting Fractions, Decimals and Percentages

Three costumes for the same number

Suppose half a pizza is left. You could say "½ of the pizza", or "0.5 of the pizza", or "50% of the pizza". All three describe the exact same amount — they are just different "costumes" for the same value. Fractions, decimals and percentages (often shortened to FDP) are three ways of writing parts of a whole.

Being able to switch between them is one of the most useful skills in maths. Prices, discounts, test scores, statistics and recipes all jump between these forms, so a fluent converter is never confused. This lesson covers every direction. For the ideas behind each form, see decimals explained and percentages made easy.

The key idea: percent means "out of 100"

The word percent literally means "per hundred". So 50% means 50 out of 100, which is the fraction 50/100, which equals the decimal 0.50. Hold on to this one idea and most conversions become obvious. The decimal point is the bridge: a percentage is simply a decimal that has been multiplied by 100.

Fraction → Decimal: divide top by bottom

A fraction bar is really a division sign. So to turn a fraction into a decimal, divide the numerator (top) by the denominator (bottom).

Worked example 1

Convert 3/4 to a decimal.

Step 1 — Set up the division: 3 ÷ 4. Step 2 — Divide. 3 does not contain 4, so we get 0.something. 30 ÷ 4 = 7 remainder 2 (0.7 so far); bring down to 20 ÷ 4 = 5. The result is 0.75.

So 3/4 = 0.75.

Worked example 2 (a repeating decimal)

Convert 1/3 to a decimal.

1 ÷ 3 = 0.333... The 3s go on forever. We write this as 0.3̇ or round it, for example 0.33. Some fractions give neat decimals and some repeat — both are correct.

Decimal → Percentage: multiply by 100

Because a percentage is "out of 100", you turn a decimal into a percentage by multiplying by 100 and adding a % sign. A shortcut for multiplying by 100 is to move the decimal point two places to the right.

Worked example 3

Convert 0.6 to a percentage. 0.6 × 100 = 60%. (Point moves two places right: 0.6 → 60.)

Worked example 4

Convert 0.375 to a percentage. 0.375 × 100 = 37.5%.

Percentage → Decimal: divide by 100

This is the reverse: divide by 100, which moves the decimal point two places to the left.

Worked example 5

Convert 25% to a decimal. 25 ÷ 100 = 0.25.

Worked example 6

Convert 8% to a decimal. 8 ÷ 100 = 0.08. (Take care: it is 0.08, not 0.8 — you must fill the empty place with a zero.)

Percentage → Fraction: put it over 100 and simplify

Since percent means "out of 100", write the number over 100, then simplify by cancelling common factors.

Worked example 7

Convert 40% to a fraction.

Step 1 — Write over 100: 40/100. Step 2 — Simplify. Both divide by 20: 40 ÷ 20 = 2 and 100 ÷ 20 = 5. So 40% = 2/5.

Decimal → Fraction: read the place value, then simplify

Write the decimal over 10, 100 or 1000 depending on how many decimal places it has (one place → /10, two places → /100, three places → /1000), then simplify.

Worked example 8

Convert 0.45 to a fraction.

Step 1 — Two decimal places, so write over 100: 45/100. Step 2 — Simplify. Both divide by 5: 45 ÷ 5 = 9 and 100 ÷ 5 = 20. So 0.45 = 9/20.

A summary of the six routes

From → To	What to do
Fraction → Decimal	Divide top by bottom
Decimal → Fraction	Write over 10/100/1000, then simplify
Decimal → Percentage	Multiply by 100, add %
Percentage → Decimal	Divide by 100, remove %
Percentage → Fraction	Write over 100, then simplify
Fraction → Percentage	Convert to a decimal first, then ×100 (or make the bottom 100)

The common conversions worth memorising

Learning these by heart will speed up almost every calculation, because you will recognise them instantly instead of working them out:

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	0.33...	33.3%
1/100	0.01	1%

Why this matters

Each form is best for a different job, which is exactly why we convert between them. Fractions are precise and exact (1/3 loses nothing, while 0.333 is rounded). Decimals are easy to type into a calculator and to add or subtract. Percentages make comparisons fair — saying "65%" instantly tells you the score is out of 100, even if one test had 20 questions and another had 50. A confident mathematician picks the most convenient costume for the task and switches whenever it helps.

Practice activity

Build your own conversion triangle.

1. Choose five values, each starting in a different form — for example 7/10, 0.8, 90%, 1/8, 0.05.
2. For each one, write the other two forms, showing your working.
3. Check your answers using the common-conversions table where it applies, and use a calculator to confirm any tricky divisions.
4. Finally, look at a real shopping receipt or a sale poster. Find a percentage discount and rewrite it as both a fraction and a decimal, then explain why the percentage form is the one shops choose to advertise.

Quick recap

Fractions, decimals and percentages are the same value in three costumes. Divide to go from fraction to decimal, multiply or divide by 100 to swap decimals and percentages, and use place value or "over 100" plus simplifying to reach fractions. Memorise the common conversions and you will move between all three forms without hesitation.