Percentage to Fraction Converter Formula

Understand the math behind the percentage to fraction converter. Each variable explained with a worked example.

Use the Percentage to Fraction Converter

Formulas Used

Simplified Numerator

numerator = round(percentage * 100) / gcd(round(percentage * 100), 10000)

Simplified Denominator

denominator = 10000 / gcd(round(percentage * 100), 10000)

Decimal Value

decimal_value = percentage / 100

Variables

VariableDescriptionDefault
percentagePercentage(%)75

How It Works

Percentage to Fraction Converter

Method

1. Write the percentage as a fraction over 100: e.g., 75% = 75/100 2. Simplify by finding the GCD of numerator and denominator 3. Divide both by the GCD

Example: 75% = 75/100, GCD(75,100)=25, so 75/25 = 3 and 100/25 = 4 → 3/4

For decimals like 12.5%, we multiply by 100 to avoid fractions in the numerator: 1250/10000, then simplify.

Worked Example

Convert 75% to a fraction.

percentage = 75
  1. 0175% = 7500/10000 (multiplied by 100 for precision)
  2. 02GCD(7500, 10000) = 2500
  3. 03Numerator = 7500 / 2500 = 3
  4. 04Denominator = 10000 / 2500 = 4
  5. 05Result: 3/4

Frequently Asked Questions

How do you convert a percentage to a fraction?

Divide the percentage by 100 to write it as a fraction (e.g., 75% = 75/100), then simplify by dividing both numerator and denominator by their GCD.

What is 33.33% as a fraction?

33.33% is approximately 1/3. Enter 33.33 to get the closest fraction approximation.

Can this handle decimal percentages?

Yes, the converter handles decimal percentages by multiplying by 100 to work with integers, then simplifying.

Ready to run the numbers?

Open Percentage to Fraction Converter