Decimal to Fraction Calculator

Enter a positive or negative decimal number

Higher values give more precise fractions but take longer to calculate

Result

Decimal Fraction Mixed Number

This calculator converts a decimal number to its equivalent fraction using the following mathematical approach:

Let x = decimal number
Multiply by 10^n where n = number of decimal places
Let numerator = x × 10^n
Let denominator = 10^n
Simplify fraction by dividing numerator and denominator by GCD

For repeating decimals, the calculator uses continued fractions to find the best approximation within the specified maximum denominator.

Example Calculation

For the decimal 0.75:

  • Count decimal places: 2
  • Multiply by 100: 0.75 × 100 = 75
  • Create fraction: 75/100
  • Simplify by dividing by GCD(75, 100) = 25
  • Result: 3/4

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Decimal to Fraction Calculator

The Decimal to Fraction Calculator converts any decimal number into its exact fractional form, including repeating decimals. Whether you’re working on math homework or dealing with precise measurements, this tool simplifies the process of expressing decimals as clean, reduced fractions.

Try it now on the Math Calculators Main Page for quick and accurate conversions between decimals and fractions.

What Is a Decimal to Fraction Calculator?

A Decimal to Fraction Calculator converts any decimal number into a fraction or mixed number. It handles both finite (terminating) and infinite (repeating) decimals with precision. For example:

  • 0.5 → 1/2
  • 0.125 → 1/8
  • 2.625 → 2 5/8

This tool also manages repeating decimals, which are decimals where one or more digits repeat endlessly (like 0.6666… or 1.8333…).

If you often work with fractions in complex math expressions, you can also try the Complex Fractions Calculator to simplify multi-layered fractions easily.

Entering Repeating Decimals

When dealing with repeating decimals, you’ll need to specify how many digits repeat. Here’s how:

  • For 0.6666…, enter 0.6 and set repeating digits = 1. Result: 2/3
  • For 0.363636…, enter 0.36 and repeating digits = 2. Result: 4/11
  • For 1.8333…, enter 1.83 and repeating digits = 1. Result: 1 5/6
  • For 0.857142857142…, enter 0.857142 and repeating digits = 6. Result: 6/7

Repeating decimals can be tricky to handle manually, which is why automated tools like this calculator are designed to apply algebraic logic quickly and correctly.

How to Convert a Negative Decimal to a Fraction

Handling negative decimals follows the same steps as positive ones, except for the sign:

  1. Remove the negative sign temporarily.
  2. Convert the positive number to a fraction.
  3. Reapply the negative sign to your result.

Mathematically, if a = b, then -a = -b.
For example:
-0.75 → -3/4

How to Convert a Decimal to a Fraction (Step-by-Step)

Let’s walk through a simple example to show the math behind it.

Step 1: Write the decimal as a fraction over 1
2.625 = 2.625/1

Step 2: Multiply numerator and denominator by 10³ (since there are 3 digits after the decimal)
(2.625 × 1000) / (1 × 1000) = 2625/1000

Step 3: Reduce the fraction by dividing numerator and denominator by their Greatest Common Factor (GCF = 125)
2625 ÷ 125 = 21
1000 ÷ 125 = 8

Fraction = 21/8

Step 4: Convert the improper fraction to a mixed number
21/8 = 2 5/8

Therefore,
2.625 = 2 5/8

For another example:
0.625 = 625/1000 = 5/8

Converting Repeating Decimals to Fractions (Algebraic Method)

To convert a repeating decimal into a fraction, you can use an algebraic method:

  1. Let x equal your repeating decimal.
    Example: x = 2.666...
  2. Identify the repeating digits (here it’s 6) and multiply both sides by 10³ = 1000.
    1000x = 2666.666...
  3. Subtract the first equation from the second:
    1000x - x = 2666.666... - 2.666...
    999x = 2664
  4. Solve for x:
    x = 2664 / 999
  5. Simplify the fraction using GCF (333):
    (2664 ÷ 333) / (999 ÷ 333) = 8/3

Thus,
2.666… = 8/3 = 2 2/3

Another Example: Convert 0.333… to a Fraction

  1. x = 0.333...
  2. Multiply both sides by 10³ = 1000.
    1000x = 333.333...
  3. Subtract: 1000x - x = 333.333... - 0.333...
    999x = 333
  4. Solve: x = 333/999 = 1/3

Therefore,
0.333… = 1/3

For problems involving identifying or simplifying patterns in numbers, the Diamond Problem Solver is a handy complementary tool to understand factor relationships visually.

Quick Summary Table

DecimalFractionMixed Number (if applicable)
0.51/2—
0.6255/8—
2.62521/82 5/8
0.333…1/3—
2.666…8/32 2/3
0.857142…6/7—

Why Converting Decimals to Fractions Matters

Fractions provide exact values, while decimals are often approximations. This makes fractions crucial in algebra, geometry, and measurement problems where precision matters.
For instance, 0.333 is only an approximation of 1/3, which repeats infinitely.

When exploring fraction relationships, you might also find the Equivalent Fractions Calculator useful—it quickly identifies equivalent values and simplifies complex ratios.

References

  • Wikipedia contributors. “Repeating Decimal,” Wikipedia, The Free Encyclopedia. Last visited 18 July, 2016.