How to Convert Fractions to Decimals to Percentages

Fractions, decimals and percentages are three different ways of writing the same thing. Once you see them as different languages for the same idea, converting between them becomes straightforward.

This guide walks through each conversion step by step with worked examples. It covers everything Australian students need for Year 7 and beyond, aligned to the Australian Curriculum.

The big picture

Think of it this way:

• 1/2 is a fraction
• 0.5 is a decimal
• 50% is a percentage

All three describe exactly the same amount. The only difference is the format. Learning to move between them is one of the most useful skills in maths because different situations call for different formats. You will see percentages on sale signs, decimals on calculators, and fractions in recipes.

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Fraction to decimal

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

Example 1

Convert 3/4 to a decimal.

Divide 3 by 4: 3 / 4 = 0.75

Example 2

Convert 2/5 to a decimal.

Divide 2 by 5: 2 / 5 = 0.4

Example 3

Convert 1/3 to a decimal.

Divide 1 by 3: 1 / 3 = 0.333... (the 3 repeats forever, so we write 0.3 recurring)

Not every fraction gives a neat decimal. When the denominator only has factors of 2 and 5, the decimal will terminate. Otherwise, it repeats. This is worth remembering because it explains why some conversions look messier than others.

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Decimal to fraction

Read the decimal using place value, then simplify.

Example 1

Convert 0.6 to a fraction.

0.6 means "6 tenths," so write it as 6/10. Simplify by dividing top and bottom by 2: 6/10 = 3/5.

Example 2

Convert 0.75 to a fraction.

0.75 means "75 hundredths," so write it as 75/100. Simplify by dividing top and bottom by 25: 75/100 = 3/4.

Example 3

Convert 0.125 to a fraction.

0.125 means "125 thousandths," so write it as 125/1000. Divide top and bottom by 125: 125/1000 = 1/8.

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Fraction to percentage

There are two reliable methods. Use whichever feels more natural.

Method 1: Convert the fraction to a decimal first, then multiply by 100.

Method 2: Multiply the fraction by 100 directly.

Example

Convert 3/8 to a percentage.

Method 1: 3 / 8 = 0.375, then 0.375 x 100 = 37.5%

Method 2: (3/8) x 100 = 300/8 = 37.5%

Both methods give the same answer. Method 1 is handy if you are comfortable with long division. Method 2 avoids decimals until the final step.

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Percentage to fraction

Write the percentage as a fraction over 100, then simplify.

Example 1

Convert 40% to a fraction.

40/100 = 2/5 (divide top and bottom by 20).

Example 2

Convert 12.5% to a fraction.

12.5/100 = 125/1000 = 1/8 (multiply top and bottom by 10 first to remove the decimal, then simplify).

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Decimal to percentage

Multiply by 100 (or equivalently, move the decimal point two places to the right).

Examples

• 0.35 x 100 = 35%
• 0.7 x 100 = 70%
• 1.2 x 100 = 120% (yes, percentages can be greater than 100)

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Percentage to decimal

Divide by 100 (or move the decimal point two places to the left).

Examples

• 85% / 100 = 0.85
• 6% / 100 = 0.06
• 150% / 100 = 1.5

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Quick reference table

Fraction	Decimal	Percentage
1/2	0.5	50%
1/4	0.25	25%
3/4	0.75	75%
1/5	0.2	20%
1/3	0.333...	33.3...%
1/8	0.125	12.5%
2/5	0.4	40%
3/10	0.3	30%

Memorising the common ones in this table saves time in tests and everyday maths.

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Common mistakes to avoid

• Forgetting to simplify fractions: 50/100 is correct, but 1/2 is the expected final answer.
• Moving the decimal the wrong way: To go from decimal to percentage, move right. To go from percentage to decimal, move left. A useful check: percentages are bigger numbers than decimals, so if your answer went the wrong direction, you moved the wrong way.
• Confusing 0.5% with 50%: 0.5% is half of one percent, which is tiny. 50% is half. Read the question carefully.

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Practice makes it automatic

These conversions come up constantly in later topics like probability, statistics, financial maths and measurement. The more fluent you are now, the less mental effort those topics will require.

If you want structured practice with these conversions, imSteyn covers fractions, decimals and percentages as part of the Year 7 curriculum. It walks you through examples, then lets you practise with guided feedback rather than just marking answers right or wrong.

The key to mastering conversions is understanding that fractions, decimals and percentages are not three separate topics. They are one idea expressed three ways. Once that clicks, the methods follow naturally.