Decimal to Fraction Converter

Convert any terminating decimal (e.g., 0.125, 3.4) into its simplest fractional form. Enter your decimal number below to get the results as a **simplified fraction**, an **improper fraction**, and a **mixed number**.

The Three Steps to Converting Decimals to Fractions

The key principle is that the place value of the last digit in the decimal determines the denominator (a power of ten) of the initial fraction.

1. Determine Initial Fraction ($A/B$): Identify the place value of the last digit in the decimal.
   • If the decimal is 0.7 (tenths place), the denominator is 10. Fraction: $\frac{7}{10}$
   • If the decimal is 0.75 (hundredths place), the denominator is 100. Fraction: $\frac{75}{100}$
   • If the decimal is 0.125 (thousandths place), the denominator is 1000. Fraction: $\frac{125}{1000}$
   The whole number part is temporarily ignored or used to convert to an improper fraction later.
2. Find the Greatest Common Divisor (GCD): The GCD is the largest number that divides evenly into both the numerator and the denominator. This is the crucial step for simplification.
3. Simplify: Divide both the numerator and the denominator by the GCD to get the simplified fraction (lowest terms).

Handling Decimals with a Whole Number

For a number like $4.3$, treat the whole number (4) and the decimal part (0.3) separately. $0.3 = \frac{3}{10}$. The mixed number is $4\frac{3}{10}$.

To find the improper fraction, convert the mixed number: $4\frac{3}{10} = \frac{(4 \times 10) + 3}{10} = \frac{43}{10}$.

Converting Repeating Decimals

This calculator primarily targets terminating decimals. Converting repeating decimals (like $0.\overline{6}$) requires a different algebraic technique:

1. Let $x$ equal the repeating decimal (e.g., $x = 0.666...$).
2. Multiply $x$ by $10^n$, where $n$ is the number of repeating digits (e.g., $10x = 6.666...$).
3. Subtract the original equation from the new one ($10x - x = 6.666... - 0.666...$).
4. Solve for $x$: $9x = 6$, so $x = \frac{6}{9}$, which simplifies to $\frac{2}{3}$.

Frequently Asked Questions (FAQ)