Converting Fractions, Decimals and Percentages: KS3 Maths Guide

Fractions, decimals, and percentages are three ways of writing the same value. To convert between them you need two key facts: a percentage is a fraction with denominator 100, and a decimal is a fraction whose denominator is a power of 10. Once you see these connections, every conversion follows a short set of steps.

The core connections

Form | Meaning | Example
Fraction | Part out of a total | 3/4 (three parts out of four)
Decimal | Fraction with denominator 10, 100, 1000, … | 0.75
Percentage | Fraction with denominator 100 | 75%

All three express the same quantity. On KS3 and GCSE papers you need to move freely between all three forms.

Converting a fraction to a decimal

Method: divide the numerator by the denominator.

A fraction a/b means "a divided by b."

Worked example 1

Convert 3/4 to a decimal.

3 ÷ 4 = 0.75

Answer: 0.75

Worked example 2

Convert 7/8 to a decimal.

7 ÷ 8:

8 goes into 70 eight times (8 × 8 = 64), remainder 6.

8 goes into 60 seven times (8 × 7 = 56), remainder 4.

8 goes into 40 five times (8 × 5 = 40), remainder 0.

7 ÷ 8 = 0.875

Answer: 0.875

Recurring decimals

Some fractions produce recurring (repeating) decimals.

1/3 = 0.333... written as 0.3̄ (a dot over the 3).

1/7 = 0.142857142857... written as 0.142857̄ (dots over the first and last digit of the repeating block).

You should know common recurring decimals by Year 9.

Converting a decimal to a fraction

Method: write the decimal as a fraction over 10, 100, 1000 (matching the number of decimal places), then simplify.

Worked example 3

Convert 0.6 to a fraction.

0.6 has one decimal place, so the denominator is 10:

0.6 = 6/10

Simplify: HCF of 6 and 10 is 2. 6/10 = 3/5.

Answer: 3/5

Worked example 4

Convert 0.35 to a fraction.

Two decimal places → denominator 100:

0.35 = 35/100

Simplify: HCF of 35 and 100 is 5. 35/100 = 7/20.

Answer: 7/20

Worked example 5

Convert 0.125 to a fraction.

Three decimal places → denominator 1000:

0.125 = 125/1000

Simplify: HCF of 125 and 1000 is 125. 125/1000 = 1/8.

Answer: 1/8

Converting a fraction to a percentage

Method: multiply the fraction by 100 and attach the % sign.

fraction × 100 = percentage

Worked example 6

Convert 3/5 to a percentage.

3/5 × 100 = 300/5 = 60

Answer: 60%

Worked example 7

Convert 7/8 to a percentage.

7/8 × 100 = 700/8 = 87.5

Answer: 87.5%

Alternatively, convert to a decimal first (Step 2 above): 7/8 = 0.875, then multiply by 100 to get 87.5%.

Converting a percentage to a fraction

Method: write the percentage over 100, then simplify.

Worked example 8

Convert 45% to a fraction.

45% = 45/100

Simplify: HCF of 45 and 100 is 5. 45/100 = 9/20.

Answer: 9/20

Worked example 9

Convert 12.5% to a fraction.

12.5% = 12.5/100

Multiply numerator and denominator by 2 to remove the decimal: 25/200.

Simplify: HCF of 25 and 200 is 25. 25/200 = 1/8.

Answer: 1/8

Converting a decimal to a percentage

Method: multiply by 100 and attach the % sign. (Equivalently, move the decimal point two places to the right.)

Worked example 10

Convert 0.07 to a percentage.

0.07 × 100 = 7

Answer: 7%

Worked example 11

Convert 1.3 to a percentage.

1.3 × 100 = 130

Answer: 130% (Percentages can exceed 100% when the quantity is more than the whole.)

Converting a percentage to a decimal

Method: divide by 100. (Equivalently, move the decimal point two places to the left.)

Worked example 12

Convert 36% to a decimal.

36 ÷ 100 = 0.36

Answer: 0.36

Key FDP conversion table

Memorising these values will save time in exams.

Fraction | Decimal | Percentage
1/2 | 0.5 | 50%
1/4 | 0.25 | 25%
3/4 | 0.75 | 75%
1/5 | 0.2 | 20%
2/5 | 0.4 | 40%
3/5 | 0.6 | 60%
4/5 | 0.8 | 80%
1/10 | 0.1 | 10%
1/3 | 0.333... | 33.3̄%
2/3 | 0.666... | 66.6̄%
1/8 | 0.125 | 12.5%
3/8 | 0.375 | 37.5%

How FDP fits the KS3 national curriculum

The Department for Education's KS3 maths programme of study requires pupils to "work interchangeably with terminating decimals and their corresponding fractions" and to interpret percentages and percentage changes as fractions or decimals. The statutory national curriculum for Key Stage 3 and 4 confirms that fluency in converting between fractions, decimals, and percentages is a prerequisite for percentage calculations, ratio problems, and the probability topics that appear throughout Year 7 to Year 9 and on into GCSE.

Common mistakes to avoid

Mistake 1 — Dividing by 10 instead of 100 when converting percentage to decimal. 36% = 0.36, not 3.6. Always divide by 100.

Mistake 2 — Forgetting to simplify the fraction. 35/100 = 7/20, not 35/100. Mark schemes at KS3 typically require fully simplified answers.

Mistake 3 — Assuming all fractions give terminating decimals. 1/3 = 0.333..., not 0.3. Only fractions whose denominator (in lowest terms) has prime factors of only 2 and 5 terminate.

Mistake 4 — Writing a percentage greater than 100 as an error. 150% = 1.5 = 3/2 is perfectly valid. It means 1.5 times the original quantity.

Frequently asked questions

What is the quickest way to convert a fraction to a percentage?

Multiply the fraction by 100. For example, 2/5 × 100 = 40%. If the denominator divides 100 neatly (denominators 2, 4, 5, 10, 20, 25, 50, 100), the arithmetic is quick. For other denominators, convert to a decimal by dividing first, then multiply by 100.

How do I convert a recurring decimal to a fraction?

For a single recurring digit such as 0.7̄ (meaning 0.777...): let x = 0.777.... Then 10x = 7.777.... Subtract: 10x − x = 7, so 9x = 7, giving x = 7/9. For two recurring digits, multiply by 100 instead. This method is taught at the top end of KS3 and appears at GCSE.

Why do I need to know FDP conversions off by heart?

On non-calculator papers you cannot rely on long division for every conversion. Knowing that 1/8 = 0.125 = 12.5% or 3/4 = 0.75 = 75% saves time and reduces errors. Exam questions often present a value in one form and require you to recognise it in another form within a multi-step problem.

Is 0.3 the same as 1/3?

No. 0.3 = 3/10, not 1/3. The fraction 1/3 = 0.333... (a recurring decimal). This is a very common misconception: the terminating decimal 0.3 is close to 1/3, but they are not equal. On a calculator, 1 ÷ 3 = 0.333333..., not 0.3.

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