Fractions, Decimals & PercentagesEdexcel GCSE Maths: Revision notes
Section 1
How do we convert between fractions and decimals?
To convert a fraction to a decimal, divide the numerator by the denominator.
- 3/8 = 3 ÷ 8 = 0.375
To convert a terminating decimal to a fraction, write the digits after the decimal point over the correct power of 10, then simplify.
- 0.35 = 35/100 = 7/20
Recurring decimals convert to fractions using algebra (see the Must Know section for the method).
Convert 0.6̇ (0.666...) to a fraction: let x = 0.666..., 10x = 6.666..., so 9x = 6, x = 6/9 = 2/3
Section 2
How do we convert between decimals and percentages?
To convert a decimal to a percentage, multiply by 100 (move the decimal point two places right) and add the % sign. To convert a percentage to a decimal, divide by 100 (move the decimal point two places left).
- 0.42 = 42%
- 7.5% = 0.075
Percentages greater than 100% correspond to decimals greater than 1, representing more than the whole amount.
Section 3
How do we convert between fractions and percentages?
To convert a fraction to a percentage, first convert to a decimal (divide numerator by denominator), then multiply by 100. Alternatively, convert the fraction to an equivalent fraction with denominator 100.
- 3/5 = 0.6 = 60%
- 17/20: multiply numerator and denominator by 5 to get 85/100 = 85%
To convert a percentage to a fraction, write it over 100 and simplify.
- 45% = 45/100 = 9/20
Memorise common conversions (1/2 = 50%, 1/4 = 25%, 1/3 = 33.3̇%, 1/5 = 20%, 1/8 = 12.5%) to save time in the exam.
Section 4
How do we order fractions, decimals and percentages?
To order a mixed list of fractions, decimals and percentages, convert everything to the same format — usually decimals, since they are easiest to compare digit by digit.
- Convert every value to a decimal
- Compare the decimals using place value
- Arrange in the required order (ascending or descending), then convert back to the original format if the question asks for it
A number line can help visualise the order, especially for values close together.
Order 0.4, 3/8, 42% from smallest to largest: convert to decimals — 0.4, 0.375, 0.42. Order: 3/8, 0.4, 42%
Section 5
How do we use these interchangeably in problem-solving?
Many exam questions mix fractions, decimals and percentages within the same problem, expecting fluent conversion. Common contexts include:
- Comparing discounts given as fractions vs. percentages
- Working out a fraction or percentage of a quantity, then converting the answer to a different format
- Interpreting percentage change as a decimal multiplier (e.g. a 15% increase multiplies by 1.15)
Both fractions and percentages can act as operators: "3/4 of" and "75% of" produce the same calculation.
Do not assume a percentage above 100% is an error — it is valid and means more than the original whole, e.g. 120% of 50 = 60.
Must Know
- Fraction → decimal: divide numerator by denominator
- Decimal → percentage: multiply by 100; percentage → decimal: divide by 100
- Fraction → percentage: convert to decimal first, then multiply by 100 (or scale to a denominator of 100)
- To order mixed values, convert them all to decimals first
- Recurring decimal to fraction: use algebra — multiply by a power of 10 to align the repeating block, then subtract
- Percentages over 100% and decimals over 1 both represent more than the whole
That's the notes covered.
Carry on to the next subtopic.