Decimal to Fraction Converter — Free Math Tool

How to Convert Decimals to Fractions

Converting a decimal to a fraction is a simple process of writing the decimal as a fraction over a power of 10, then simplifying. Follow these steps:

1. Enter the decimal value — Input any terminating decimal number (e.g., 0.625).
2. Click “Convert to Fraction” — The tool will calculate the simplified fraction, the unsimplified version, and the mixed number equivalent.
3. Follow the steps — The step-by-step solution shows the multiplier used to clear the decimal and how the Greatest Common Divisor (GCD) is used to simplify the terms.

The Formula for Decimal to Fraction Conversion

To convert a decimal to a fraction manually, use the following rules:

1. Determine the number of decimal places (digits to the right of the decimal point), let’s call this d.
2. Write the fraction as: Numerator = Number × 10ᵈ and Denominator = 10ᵈ.
3. Find the Greatest Common Divisor (GCD) of the Numerator and Denominator.
4. Divide both parts by the GCD to simplify the fraction to its lowest terms.

For example, to convert 0.75:

• Number of decimal places: 2 (so we multiply by 10² = 100)
• Unsimplified fraction: 75/100
• GCD of 75 and 100 is 25
• Simplify: (75 ÷ 25) ÷ (100 ÷ 25) = 3/4

Practical Conversion Examples

Example 1: 0.125 to Fraction

Decimal places = 3. Multiply by 1,000 to get 125/1000. The GCD of 125 and 1000 is 125. (125 ÷ 125) ÷ (1000 ÷ 125) = 1/8. Result: 1/8.

Example 2: 2.50 to Fraction (Mixed Number)

Multiply by 100 to get 250/100. Simplify by dividing by the GCD of 50 to get 5/2. In mixed number form, this is 2 1/2.

Example 3: 0.3333… (Repeating Decimals)

Terminating decimal converters are designed for terminating decimals (like 0.333). To convert repeating decimals (like 0.333…), different formulas apply: x = 0.333... → 10x = 3.333... → 9x = 3 → x = 3/9 = 1/3.

Frequently Asked Questions

What is a terminating decimal?

A terminating decimal is a decimal number that has a finite number of digits after the decimal point (e.g., 0.5, 0.25, 0.1234). Repeating or infinite decimals continue indefinitely (e.g., 0.333… or π).

How do I convert a negative decimal?

The conversion process is identical. Carry the negative sign through the calculation and place it on the numerator of the final simplified fraction.

What is the difference between a proper fraction and an improper fraction?

A proper fraction has a numerator that is smaller than its denominator (e.g., 3/4). An improper fraction has a numerator that is larger than or equal to its denominator (e.g., 5/2). Improper fractions can also be written as mixed numbers (e.g., 2 1/2).

Can all decimals be written as fractions?

Only rational numbers (decimals that terminate or repeat in a regular pattern) can be written as fractions. Irrational numbers (like the square root of 2 or Pi) cannot be written as simple fractions.