Understand fractions, decimals and percentages
A fraction describes a ratio, a decimal uses place value, and a percentage expresses the ratio out of 100. One quarter, 0.25 and 25% represent the same proportion.
Decimal to percentage
Multiply a decimal by 100 and add the percent sign. For example, 0.375 × 100 = 37.5%. A decimal greater than one becomes a percentage above 100%: 1.2 is 120%.
Percentage to decimal
Divide the percentage by 100. The result of converting 7.5% is 0.075, not 0.75. This is a common source of a tenfold error when calculating small rates.
Fraction to percentage
Divide the numerator by the denominator, then multiply by 100. For 3/8, calculate 3 ÷ 8 = 0.375, then 37.5%. The denominator must not be zero.
Percentage to fraction
Write the percentage over 100, then simplify. For 12.5%, start with 12.5/100, multiply both numerator and denominator by 10 to get 125/1000, then reduce to 1/8.
Rounding fractions, decimals and percentages
One third is 0.333… and therefore 33.333…%. Writing 33.33% is a rounded approximation. Multiplying that rounded percentage by three gives 99.99%, so a tiny gap does not mean the exact fractions fail to sum to one whole.
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 1/8 | 0.125 | 12.5% |
| 1/3 | 0.333… | 33.333…% |
Compare exact values with rounded displays
Suppose you need to compare one sixth with 16.7%. Dividing one by six produces a repeating decimal of approximately 0.1666667. Converting 16.7% to a decimal gives 0.167. The second value is slightly larger, even though both might appear similar on a short display. Keep an exact fraction where possible until the calculation is complete, particularly when several operations follow.
For a simple addition, consider one quarter plus three eighths. Express both with a common denominator: two eighths plus three eighths equals five eighths. The decimal is 0.625 and the corresponding rate is 62.5%. Adding rounded displays can also work for an estimate, but it may introduce a small difference compared with working from the exact values.
Choose a useful representation
Fractions are convenient when the relationship has a simple exact denominator, such as one half or three quarters. Decimals are convenient for multiplication and comparison on a common place-value scale. A rate out of one hundred is convenient when explaining shares to readers. Choose the representation that makes the question easier to understand, then label it clearly.
Check the input label before typing. A field asking for a rate expects 25 for 25%, while a decimal multiplier uses 0.25. Confusing these formats changes the result by a factor of one hundred. An estimate using a familiar share can reveal that mistake before you rely on an answer.
Put the method into practice
Choose the percentage calculator for parts and wholes, or use the percentage change calculator for movement from an original value. For a sale price, the discount calculator and reverse percentage calculator answer two different questions.
Questions to check before calculating
Which number is the reference?
Identify the whole or original amount before calculating. If neither value is the natural reference, consider whether a mean-based percentage difference fits your question.
Should I round intermediate values?
For a mathematical result, keep intermediate precision and round the final display. Actual transaction rules may require a particular rounding policy.
Can I use this as an official grade or financial determination?
These guides explain arithmetic. Institutional grading rules, financial policies and legal requirements must be checked separately.
Take the formula with you
Write the question in words, label the known values and choose the denominator deliberately. Check the answer with an estimate or by reversing the calculation. A short explanation alongside the number makes the result easier to understand and less likely to be misused.