Fractions, Decimals and Percentages Revision Notes for Edexcel GCSE Maths

Fractions, decimals and percentages

Understanding the relationship

All three forms - fractions, decimals, and percentages - represent the same mathematical concept: proportion. They are simply three equivalent methods of expressing a portion or part of something. Understanding that they are closely related and completely interchangeable is crucial for working with them effectively.

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The key insight is that these are not three separate mathematical concepts, but rather three different ways of expressing the exact same mathematical relationship. This means you can always convert between them when solving problems.

Essential conversion table

The following conversions are so fundamental that you should memorise them completely. This will save you time and help you work more efficiently in exams.

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Critical Conversions to Memorise:

Fraction	Decimal	Percentage
1/2	0.5	50%
1/4	0.25	25%
3/4	0.75	75%
1/3	0.333333…	33⅓%
2/3	0.666666…	66⅔%
1/10	0.1	10%
2/10	0.2	20%
1/5	0.2	20%
2/5	0.4	40%

The more of these conversions you learn by heart, the better your mathematical fluency will become. However, for those conversions you don't immediately remember, you must understand how to convert between the three forms.

Converting between fractions, decimals and percentages

From fraction to decimal

To convert a fraction to a decimal, simply divide the numerator (top number) by the denominator (bottom number).

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Worked Example: Converting Fraction to Decimal

Convert $\frac{7}{20}$ to a decimal:

$\frac{7}{20} = 7 ÷ 20 = 0.35$

From decimal to percentage

To convert a decimal to a percentage, multiply by 100.

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Worked Example: Converting Decimal to Percentage

Convert $0.35$ to a percentage:

$0.35 × 100 = 35%$

From percentage to decimal

To convert a percentage to a decimal, divide by 100.

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Worked Example: Converting Percentage to Decimal

Convert $35%$ to a decimal:

$35% ÷ 100 = 0.35$

From decimal to fraction (the tricky one)

Converting decimals to fractions requires different approaches depending on the type of decimal you're working with.

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This conversion is often considered the most challenging because it requires you to recognise patterns in decimal numbers and apply different methods based on whether the decimal terminates or recurs.

Converting terminating decimals to fractions

Terminating decimals are those that end after a certain number of decimal places (like $0.6$ , $0.25$ , $0.345$ ). For these conversions, use this straightforward method:

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Worked Example: Converting Terminating Decimals

Method:

Place the digits after the decimal point as the numerator (top number)
Use a power of 10 as the denominator (bottom number)
The power of 10 should have the same number of zeros as there were decimal places

Examples:

$0.6 = \frac{6}{10}$
$0.3 = \frac{3}{10}$
$0.7 = \frac{7}{10}$
$0.12 = \frac{12}{100}$
$0.78 = \frac{78}{100}$
$0.05 = \frac{5}{100}$
$0.345 = \frac{345}{1000}$
$0.908 = \frac{908}{1000}$
$0.024 = \frac{24}{1000}$

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Don't Forget to Simplify!

Remember that these fractions can often be simplified by cancelling down to their simplest form. For example, $\frac{6}{10} = \frac{3}{5}$ and $\frac{12}{100} = \frac{3}{25}$ .

Converting recurring decimals to fractions

Recurring decimals (like $0.333333...$ or $0.666666...$ ) require a more complex method for conversion to fractions. This is generally more challenging and requires specific techniques that build on the basic principles covered here.

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Recurring decimal conversions involve algebraic manipulation and are typically covered in more advanced topics. The key is to first master the terminating decimal conversions before attempting these more complex cases.

Practical approach to conversions

When faced with conversion problems, remember that you can move between any two forms by going through the third if needed.

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Flexible Conversion Strategy

For instance, if you need to convert a percentage to a fraction, you might find it easier to convert the percentage to a decimal first, then convert that decimal to a fraction. This step-by-step approach can make complex conversions more manageable.

Remember!

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Key Points to Remember:

Fractions, decimals, and percentages all represent the same concept: proportion
Learn the common conversion table by heart to improve your speed and accuracy
To convert fraction to decimal: divide the numerator by the denominator
To convert decimal to percentage: multiply by 100
To convert percentage to decimal: divide by 100
For terminating decimals to fractions: put the decimal digits over the appropriate power of 10
Always check if your final fraction can be simplified to its lowest terms

Fractions, Decimals and Percentages (Edexcel GCSE Maths): Revision Notes