Decimal to Fraction Calculator

How to Convert a Decimal to a Fraction

Converting a terminating decimal to a fraction uses the place-value system of decimal numbers. Every digit after the decimal point represents a fraction of a power of 10:

• 1 decimal place → denominator is 10
• 2 decimal places → denominator is 100
• 3 decimal places → denominator is 1,000
• and so on…

Step-by-Step Method

Here is the full process for converting 0.625 to a fraction:

Step 1: Count the decimal places. There are 3 digits after the decimal point.

$$0.625 = \dfrac{625}{1000}$$

Step 2: Find the GCD of the numerator and denominator.

$$\gcd(625,\ 1000) = 125$$

Step 3: Divide both parts by the GCD.

$$\dfrac{625 \div 125}{1000 \div 125} = \dfrac{5}{8}$$

Whole Number Part

For decimals greater than 1 (like 2.5), the whole-number part stays as-is and the decimal part is converted separately, then combined:

$$2.5 = 2 + 0.5 = 2 + \dfrac{1}{2} = \dfrac{5}{2} = 2\dfrac{1}{2}$$

Repeating Decimals

Repeating decimals like \(0.\overline{3}\) cannot be entered directly as "0.333…" — the computer stores only a finite number of digits. If you enter enough repetitions (e.g. 0.333333), the calculator will usually find the closest simple fraction, but for the exact result use algebra:

Let \(x = 0.\overline{3}\). Then \(10x = 3.\overline{3}\), so \(10x - x = 3\), giving \(9x = 3\) and \(x = \dfrac{1}{3}\).

For a common repeating decimal, the Fraction to Decimal Calculator can confirm the conversion in the other direction.

Common Decimal-to-Fraction Conversions

Decimal	Fraction	Simplified
0.1	\(\frac{1}{10}\)	\(\frac{1}{10}\)
0.25	\(\frac{25}{100}\)	\(\frac{1}{4}\)
0.5	\(\frac{5}{10}\)	\(\frac{1}{2}\)
0.75	\(\frac{75}{100}\)	\(\frac{3}{4}\)
0.125	\(\frac{125}{1000}\)	\(\frac{1}{8}\)
0.375	\(\frac{375}{1000}\)	\(\frac{3}{8}\)
0.625	\(\frac{625}{1000}\)	\(\frac{5}{8}\)
0.2	\(\frac{2}{10}\)	\(\frac{1}{5}\)

Related Calculators

• Fraction to Decimal Calculator — go in the other direction: convert a fraction to a decimal
• Fraction Calculator — add, subtract, multiply, or divide fractions
• Simplify Fraction — reduce any fraction to lowest terms

Frequently Asked Questions

What if my decimal has many digits?

The calculator uses the exact digits you enter. A decimal with many digits will produce a large numerator and denominator before simplification, but the GCD step reduces it to lowest terms. If you know the decimal is repeating, the simplified result will be the exact fraction.

Can this convert negative decimals?

Yes. Enter the minus sign at the start, e.g. -0.75 converts to \(-\dfrac{3}{4}\).

What about whole numbers like 3 or -2?

Whole numbers are valid input. They will be expressed as a fraction with denominator 1, e.g. \(\dfrac{3}{1}\), and shown as the whole number itself.

How do I handle a number like 1.25?

Enter it as-is: 1.25. The calculator converts the full value to \(\dfrac{5}{4}\) and also shows the mixed number form \(1\,\dfrac{1}{4}\).