Converting Between Fractions, Decimals and Percentages
Fractions, decimals and percentages are three ways of writing the same number, and being able to move between them quickly and correctly matters far beyond the "Comparing Quantities" chapter it is first taught in — percent composition, percent yield, concentration percentages and percentage error all depend on this exact skill. This guide covers all four conversion directions, including the one most students find hardest: turning a recurring decimal back into a fraction.
The three basic conversions
Decimal → Percentage: multiply by 100
Percentage → Decimal: divide by 100
Percentage → Fraction: write as (percentage)/100, then simplify to lowest terms
Worked example 1 — fraction to decimal to percentage
Convert 3/8 to a decimal, then to a percentage.
3 ÷ 8 = 0.375
0.375 × 100 = 37.5%
Worked example 2 — percentage to simplest fraction
Convert 62.5% to a decimal and then to its simplest fraction.
62.5 ÷ 100 = 0.625
0.625 = 625/1000. Divide numerator and denominator by their common factor, 125:
625 ÷ 125 = 5, 1000 ÷ 125 = 8.
62.5% = 5/8
Worked example 3 — a quick shortcut when the denominator divides 100
Convert 7/20 to a percentage without long division.
Since 20 × 5 = 100, multiply both numerator and denominator by 5: 7/20 = 35/100.
7/20 = 35%
This shortcut works whenever the denominator is a factor of 100 (2, 4, 5, 10, 20, 25, 50) — much faster than dividing out a decimal first.
Worked example 4 — converting a recurring decimal to a fraction
Convert 0.41666... (the 6 repeats forever) to a fraction.
Let x = 0.41666...
Multiply by 100: 100x = 41.6666...
Multiply by 1000: 1000x = 416.6666...
Subtract the first from the second: 1000x − 100x = 416.6666... − 41.6666... = 375, so
900x = 375.
x = 375/900. Divide numerator and denominator by 75: 375 ÷ 75 = 5, 900 ÷ 75 = 12.
0.41666... = 5/12
Check by dividing back: 5 ÷ 12 = 0.41666... — confirmed.
Common mistakes that cost marks
- Multiplying instead of dividing (or vice versa) when moving between decimal and percentage — remember: percentage is always the larger-looking number, so decimal-to-percentage multiplies.
- Leaving a fraction unsimplified — a correct but unsimplified fraction like 625/1000 can lose marks where "simplest form" is explicitly asked for.
- Choosing the wrong power of 10 when converting a recurring decimal — the power must match how many digits repeat, and where the repeating block starts, or the subtraction step will not cancel the repeating part cleanly.
- Forgetting the % sign changes the base — 62.5% is not the same number as the decimal 62.5; it must first be divided by 100.
Where this is tested
| Level | Typical use |
|---|---|
| CBSE Class 6–8 — Fractions, Decimals, Comparing Quantities | Direct conversion and simplification questions |
| Class 10 and CUET quantitative reasoning | Fast conversion under time pressure, often combined with ratio problems |
| Class 11–12 Chemistry | Percent composition, percent yield and concentration-percentage calculations |
Check your conversion instantly. Use the calculator suite to verify a division or simplification before writing your final answer.
Open the Chemistry Calculator Suite →