Percentage to Fraction/Decimal Converter

Convert between percentages, fractions and decimals.

Overview

Converts percentages into reduced rational fractions, mixed numbers, and decimals with step-by-step simplification breakdowns.

Formula & Calculation Method

Fraction = Percentage / 100 | Simplified = (Numerator / GCD) / (Denominator / GCD)

Eliminates decimal points in percentage numerators and divides by greatest common factors to produce proper fractions.

Worked Example: Converting 37.5% into a Fraction

Inputs: Percentage = 37.5%

  • Express as fraction over 100: 37.5 / 100
  • Multiply numerator and denominator by 10 to eliminate decimal: 375 / 1000
  • Find Greatest Common Divisor: GCD(375, 1000) = 125
  • Divide by GCD: (375 / 125) / (1000 / 125) = 3/8

Summary: 37.5% = 3/8 | Decimal = 0.375 | Simplification Factor = 125

Common Use Cases

  • Arithmetic Problem Solving: Convert percentage test scores into simplified fractional proportions.
  • Financial Discount Ratios: Express percentage sale markdowns as clean fractional ratios.
  • Culinary Scaling: Convert percentage baker's percentages into exact measurement cup fractions.

Frequently Asked Questions

How do I convert a percentage with a decimal to a fraction?

Multiply numerator and denominator by 10 for every decimal place, then reduce by their greatest common divisor.

What is 0.25% as a fraction?

0.25 / 100 = 25 / 10,000 = 1 / 400.

What is 100% as a fraction?

100 / 100 = 1/1 (or the whole integer 1).

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