Formula
\text{Percentage} = \frac{\text{Part}}{\text{Whole}}\times 100\%
Used to calculate: What one portion one number is of another, to express test scores, find sale discounts, or track statistics.
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What Is the Percentage Formula?
The percentage formula is used to find what one portion of a whole is represented as a percentage. it works by dividing the part by the whole and then multiplying the result by 100. This converts the ratio between the part and the whole into a percentage that can be easily understood and compared.
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Formula and Variables
\text{Percentage} = \frac{\text{Part}}{\text{Whole}}\times 100\%| Symbol | Meaning | Unit |
| Percentage | The percentage value being calculated. | % |
| Part | The portion or amount being compared to the whole. | Same as whole |
| Whole | The total amount that the part belongs to. | Same as part |
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How to Use the Formula
To use the percentage formula, divide the the part by the whole and multiply the result by 100. The resulting number is the percentage that the part represents of the whole.
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When Is This Formula Used?
The percentage formula is used whenever you want to express one amount as a percentage of a total. It is commonly used with grades, discounts, statistics, finances, measurements, and many other everyday calculations.
Common uses:
– Grades
– Finances
– Measurements
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Important Notes
– The part and the whole must use the same units. When divided, these units cancel, making the resulting percentage dimensionless and expressed using the percent sign (%).
– The whole must be nonzero, and the part and whole should represent comparable quantities measured using the same units.
– The part and whole must be expressed in the same units before applying the formula. the resulting percentage is expressed as %.
– A percentage is not the same as a decimal. For example, 0.25 is equivalent to 25%, because the ratio must be multiplied by 100 to express it as a percentage.
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Alternate Forms
Alternate form:
\text{Part} = \frac{\text{percentage}}{100\%} \times\text{whole}Alternate form:
\text{Whole} = \frac{\text{Part} \times 100\%}{\text{Percentage}}Alternate form:
\frac{\text{Percentage}}{100\%} = \frac{\text{Part}}{\text{Whole}}—
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