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Decimal to Fraction Converter

To convert a decimal to a fraction, write the decimal over 1, multiply the numerator and denominator by 10 for each digit after the decimal point, then simplify by dividing both by their greatest common divisor. For example, 0.75 becomes 75/100, which simplifies to 3/4. Use the free calculator below for instant results with step-by-step working.

Decimal to fraction conversion is the process of rewriting a decimal number (like 0.25 or 0.333…) as a ratio of two integers. Every terminating decimal and every repeating decimal can be expressed as an exact fraction. Non-repeating, non-terminating decimals (like π) are irrational and cannot.

Decimal to Fraction Converter

For repeating decimals, use a bar notation like 0.3... or 0.16~

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Step-by-Step Solution

How Do You Convert a Decimal to a Fraction?

Converting decimals to fractions is a foundational math skill used in cooking, engineering, finance, and everyday measurements. The method depends on whether the decimal terminates (ends) or repeats infinitely. Both types always produce a rational number that can be expressed as a fraction.

How Do You Convert a Terminating Decimal to a Fraction?

A terminating decimal has a finite number of digits after the decimal point — for example, 0.75, 0.4, or 0.125. Converting one to a fraction takes three steps:

  1. Write the decimal over 1. Start by expressing the decimal as a fraction with a denominator of 1. For instance, 0.75 / 1.
  2. Multiply to remove the decimal point. Multiply both the numerator and denominator by 10 for each digit after the decimal point. Since 0.75 has two decimal places, multiply both by 100: 75 / 100.
  3. Simplify. Divide both the numerator and denominator by their greatest common divisor (GCD). The GCD of 75 and 100 is 25, so 75 ÷ 25 = 3 and 100 ÷ 25 = 4. The result is 3/4.

Example: Convert 0.625 to a fraction.

0.625 has three decimal places → multiply by 1000 → 625 / 1000. GCD(625, 1000) = 125. So 625 ÷ 125 = 5 and 1000 ÷ 125 = 8. Answer: 5/8.

How Do You Convert a Repeating Decimal to a Fraction?

A repeating decimal has one or more digits that repeat forever, like 0.333... (which equals 1/3) or 0.1666... (which equals 1/6). The algebraic method works by eliminating the repeating part:

  1. Let x equal the repeating decimal. For example, let x = 0.333....
  2. Multiply by a power of 10 that shifts one complete repeating block past the decimal point. Here, multiply by 10: 10x = 3.333....
  3. Subtract the original equation. 10x – x = 3.333... – 0.333..., which gives 9x = 3.
  4. Solve for x and simplify. x = 3/9 = 1/3.

Example: Convert 0.272727... to a fraction.

Let x = 0.272727.... The repeating block "27" has two digits, so multiply by 100: 100x = 27.2727.... Subtract: 99x = 27. So x = 27/99 = 3/11. Answer: 3/11.

If you'd like to go the other direction, use our Fraction to Decimal Converter or read the full guide on how to convert fractions to decimals.

What Are the Most Common Decimal-to-Fraction Conversions?

This quick-reference table covers the 20 most frequently searched conversions. Bookmark it or print it out for homework and kitchen math.

DecimalFractionSimplified
0.11/101/10
0.125125/10001/8
0.1666…—1/6
0.22/101/5
0.2525/1001/4
0.33/103/10
0.333…—1/3
0.375375/10003/8
0.44/102/5
0.55/101/2
0.66/103/5
0.625625/10005/8
0.666…—2/3
0.77/107/10
0.7575/1003/4
0.88/104/5
0.833…—5/6
0.875875/10007/8
0.99/109/10
1.515/103/2

Need to convert fractions the other way around? Try our Fraction to Percent Converter or return to the Master Fractions Calculator for all operations.

Frequently Asked Questions

0.75 as a fraction is 3/4. You get this by writing 75/100 and then simplifying — divide both the numerator and denominator by their greatest common divisor, which is 25. This is one of the most commonly used decimal-to-fraction conversions in cooking and measurement.
0.5 as a fraction is 1/2. Write 5/10, then divide both the numerator and denominator by 5. Because 0.5 is exactly half of 1, it equals one-half — the simplest and most widely recognized fraction.
The terminating decimal 0.33 equals 33/100 exactly. However, the repeating decimal 0.333… (with the 3 repeating forever) equals 1/3. The difference matters: 33/100 is a close approximation, while 1/3 is the exact value of the infinitely repeating form.
Let x equal the repeating decimal, then multiply x by a power of 10 that shifts one full repeating block past the decimal point. Subtract the original equation to eliminate the repeating part, then solve for x and simplify. For example, for 0.333…: let x = 0.333…, then 10x = 3.333…, subtract to get 9x = 3, so x = 1/3.
Every terminating decimal and every repeating decimal can be expressed as a fraction — a ratio of two integers. However, non-repeating, non-terminating decimals like π (3.14159…) and √2 (1.41421…) are irrational numbers and cannot be written as an exact fraction.
0.125 as a fraction is 1/8. Write 125/1000, then divide both the numerator and denominator by their GCD, which is 125. This conversion appears frequently in woodworking and engineering where eighth-inch measurements are standard.
0.625 as a fraction is 5/8. Write 625/1000, find the greatest common divisor (125), and divide both parts. As a check, 5 divided by 8 on a calculator returns exactly 0.625, confirming the conversion is correct.
A terminating decimal has a finite number of digits after the decimal point, like 0.25 or 0.8. A repeating decimal has one or more digits that cycle forever, like 0.333… or 0.142857…. Both types are rational numbers, meaning both can always be expressed as a fraction of two integers.
Write the decimal over 1, then multiply both the top and bottom by 10 for every digit after the decimal point. For 0.4, that gives 4/10. Next, simplify by finding the largest number that divides evenly into both — here it is 2 — to get 2/5. No calculator needed.
Yes. Convert the absolute value of the decimal to a fraction using the standard method, then apply the negative sign to the numerator. For example, −0.6 becomes −6/10, which simplifies to −3/5. The negative sign can be placed on the numerator, denominator, or in front of the fraction — all three forms are equivalent.

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