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Decimal to Fraction Calculator

Convert any decimal number to a fraction in its simplest form. Supports terminating decimals (0.75) and repeating decimals (0.333..., 0.142857...).

Enter a decimal. For repeating decimals, append ... or use the repeating block field below.

Append "..." to indicate a repeating decimal (e.g. 0.333...)

Leave blank for terminating decimals.

How to Convert Repeating Decimals

For a purely repeating decimal like 0.333...:

Let x = 0.333...
10x = 3.333...
10x − x = 3 → 9x = 3 → x = 3/9 = 1/3

Frequently Asked Questions

A terminating decimal has a finite number of digits after the decimal point, such as 0.25 or 1.375. These always convert to fractions with denominators that are powers of 2 and/or 5.

A repeating decimal has one or more digits that repeat infinitely, like 0.333... = 1/3 or 0.142857142857... = 1/7. Every rational number is either terminating or repeating.

Divide both the numerator and denominator by their GCF (Greatest Common Factor). For example, 6/8 → GCF(6,8)=2 → 3/4.

A mixed number combines a whole number and a proper fraction, such as 1 3/4. It is used when the decimal value is greater than 1.

Only rational numbers can be written as fractions. Irrational numbers like π (3.14159...) and √2 (1.41421...) have non-terminating, non-repeating decimals and cannot be expressed as fractions.

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