These questions ask you to recognise the same value written as a percentage, fraction or decimal. The reliable approach is to follow the direction of conversion and then check whether the size of the result makes sense.
Choose the direction before calculating
A percentage is a number of hundredths, so remove the percentage sign and divide by 100 to get a decimal. For example, 175% becomes 175 / 100 = 1.75. In the other direction, multiply a decimal by 100 and attach the percentage sign: 0.31 x 100 = 31%. These operations preserve the value; they only change its form.
For a fraction, divide the numerator by the denominator first, then multiply the decimal by 100. For example, 11/20 = 0.55, so 11/20 = 55%. You can also calculate 11 / 20 x 100 directly. Keep the numerator and denominator in their original order.
| Starting form | Method | Size check |
|---|---|---|
| Percentage to decimal | Divide the percentage number by 100. | A percentage below 100% gives a decimal below 1; a percentage above 100% gives a decimal above 1. |
| Decimal to percentage | Multiply the decimal by 100 and use the percentage sign. | A decimal between 0 and 1 gives a percentage between 0% and 100%. |
| Fraction to percentage | Divide numerator by denominator, then multiply by 100. | A proper fraction gives less than 100%; an improper fraction can give more than 100%. |
Estimate before trusting the digits. A fraction close to one should produce a percentage close to 100%, while a very small fraction should stay below 1% when its value is less than one hundredth. Unless rounding is requested, keep an exact terminating decimal rather than replacing it with a convenient estimate.
Avoid these conversion traps
| Tempting route | How to reject it |
|---|---|
| Move the decimal only one place, leave the number unchanged, or move it in the wrong direction. | The scale factor is exactly 100. Write either division by 100 or multiplication by 100 before moving any digits. |
| Read the numerator or denominator as though it were already a percentage. | A fraction describes division. Calculate numerator / denominator first; neither printed number alone usually describes the fraction's share. |
| Choose the complementary share instead of the stated share. | Converting a form does not switch to what remains. Use 100% minus the share only when the wording actually asks for the remainder. |
| Replace an exact conversion with a nearby rounded estimate. | Use the estimate as a reasonableness check, then calculate the exact value. Round only when the instruction specifies a level of precision. |
Try it
A recipe uses 0.46 of a full batch of fruit puree. Write 0.46 as a percentage. Enter the number of percent.
A battery delivers 230% of a reference energy level during a test. Write 230% as a decimal. Enter the decimal number.
A tram has completed 7/20 of its route. Write this fraction as a percentage. Enter the number of percent.