~/tools/percent-to-fraction-decimal $ run math --percentage-converter
Percent to Fraction & Decimal Converter
Convert any percentage value into its precise simplified fraction and decimal representations.
A percent to fraction and decimal converter divides the percent by 100 to yield the exact decimal, and reduces the rational fraction (Percent / 100) to its lowest terms.
Decimal Representation:
0.65
Formula: 65 / 100
Simplified Fraction:
13/20
Formula: 65/100 reduced by GCD
// How to Convert Percentages to Fractions & Decimals
Percentages, fractions, and decimals are different ways to express the same mathematical proportion. Understanding how to transition between these types is fundamental for algebra, statistics, chemistry stoichiometry, and accounting fields.
Mathematical Formulas:
Decimal = Percent / 100
Fraction = Simplify (Percent / 100) using GCD
Worked Example 1: Converting 65%
Suppose you want to convert 65% to a fraction and decimal:
1. For decimal: 65 / 100 = 0.65.
2. For fraction: Write as 65/100. Find the GCD of 65 and 100, which is 5.
3. Divide both parts by the GCD: (65 / 5) / (100 / 5) = 13/20.
Result: 65% = 0.65 = 13/20.
Worked Example 2: Converting a decimal percent (12.5%)
Suppose you have a rate like 12.5%:
1. Decimal: 12.5 / 100 = 0.125.
2. Fraction: Write as 12.5 / 100. Scale both by 10 to clear decimals: 125 / 1000.
3. Find the GCD of 125 and 1000, which is 125.
4. Divide both by 125: (125 / 125) / (1000 / 125) = 1/8.
Result: 12.5% = 0.125 = 1/8.
// Frequently Asked Questions
▸What is the easiest way to convert a percent to a decimal?
Divide the percentage by 100, which is equivalent to moving the decimal point exactly two places to the left. For example, 7% becomes 0.07.
▸What is the Greatest Common Divisor (GCD)?
The GCD is the largest positive integer that divides both the numerator and the denominator of a fraction without leaving a remainder. It is the key to simplifying fractions.
▸Does this converter support percentages larger than 100%?
Yes. For example, entering 250% yields a decimal of 2.5 and an improper fraction of 5/2 (which simplifies from 250/100).