Fractions, Decimals & Percentages Explained
Fractions, decimals and percentages are three different ways of writing the same idea: a part of a whole. Half a pizza can be written as 1/2, 0.5 or 50%. Understanding how to move between these forms is a core skill for CBSE and ICSE exams and for everyday life, from discounts to marks. This guide explains each form and shows simple conversion methods with worked examples.
The three forms explained
- Fraction: a number written as one whole over another, like 3/4. The top is the numerator, the bottom is the denominator.
- Decimal: a number using a decimal point, like 0.75, based on tenths, hundredths and so on.
- Percentage: a fraction out of 100, written with the % sign, like 75%.
Converting fractions to decimals
Divide the numerator by the denominator. To convert 3/4 to a decimal, calculate 3 ÷ 4 = 0.75. Similarly, 1/8 = 1 ÷ 8 = 0.125. Some fractions give repeating decimals, for example 1/3 = 0.333..., written as 0.3 with a bar over the 3.
Converting decimals to fractions
Write the decimal over a power of 10, then simplify. For 0.75, write 75/100, then divide top and bottom by 25 to get 3/4. For 0.6, write 6/10, then simplify to 3/5. The number of decimal places tells you the power of 10: two places means hundredths.
Converting fractions and decimals to percentages
To turn a fraction or decimal into a percentage, multiply by 100 and add the % sign.
- Decimal to percentage: 0.75 × 100 = 75%.
- Fraction to percentage: 3/4 = 0.75 = 75%, or directly (3 ÷ 4) × 100 = 75%.
- Another example: 1/5 = 0.2 = 20%.
Converting percentages back
To turn a percentage into a decimal, divide by 100: 40% = 40 ÷ 100 = 0.4. To turn it into a fraction, write it over 100 and simplify: 40% = 40/100 = 2/5. So 40% = 0.4 = 2/5, all the same value.
A worked exam-style example
Suppose a student scores 18 out of 24 in a test. As a fraction that is 18/24, which simplifies to 3/4 (dividing both by 6). As a decimal, 3 ÷ 4 = 0.75. As a percentage, 0.75 × 100 = 75%. So the student scored 75%. Being able to switch forms quickly helps you check answers and solve word problems faster.
Quick reference values worth memorising
Knowing these by heart saves time: 1/2 = 0.5 = 50%, 1/4 = 0.25 = 25%, 3/4 = 0.75 = 75%, 1/5 = 0.2 = 20%, and 1/10 = 0.1 = 10%.
These conversions are the backbone of percentage, profit-and-loss and statistics chapters in Class 9 Maths and continue into data handling in Class 10 Maths. To memorise the key reference values painlessly, try our tips on how to memorise maths formulas.
Frequently asked questions
How do I convert a fraction to a percentage quickly?
Divide the numerator by the denominator to get a decimal, then multiply by 100. For example, 3/4 = 0.75, and 0.75 × 100 = 75%.
Why are fractions, decimals and percentages important?
They all describe parts of a whole and appear constantly in exams and daily life, such as discounts, interest and test scores. Being fluent in all three lets you solve problems flexibly.
What is 0.5 as a fraction and a percentage?
The decimal 0.5 equals the fraction 1/2 and the percentage 50%. All three represent exactly one half of a whole.