Decimal to Fraction

Convert decimals to fractions or mixed numbers. Handles terminating and repeating decimals with step-by-step solutions.

Convert decimals to fractions or mixed numbers instantly. Supports both terminating and repeating decimals with step-by-step solutions.

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help_outlineHow to Useexpand_more

Turn any decimal into its fractional equivalent with this converter. When working with repeating decimals, simply indicate how many trailing digits form the repeating pattern to get the precise fraction.

How to Enter Repeating Decimals:

0.666... → Type 0.6, pick 1 digit repeats → Answer: 2/3
0.363636... → Type 0.36, pick 2 digits repeat → Answer: 4/11
1.8333... → Type 1.83, pick 1 digit repeats → Answer: 1 5/6
0.857142857142... → Type 0.857142, pick 6 digits repeat → Answer: 6/7

Handling Negative Decimals:

  1. Remove the minus sign first
  2. Convert the positive value normally
  3. Add the minus sign back to your fraction

For example: -0.75 → convert 0.75 → get 3/4 → final answer: -3/4

infoWhat is Decimal to Fraction?expand_more

This calculator changes decimal numbers into their fraction equivalents. Any decimal that ends (like 0.25) becomes a fraction over a power of ten. Decimals that go on forever with a repeating pattern (like 0.333...) also have exact fraction forms that this tool can calculate.

Two Kinds of Decimals:

Terminating Decimals

Stop after a certain number of digits

Like: 0.5, 0.75, 2.625

Repeating Decimals

One or more digits repeat endlessly

Like: 0.333..., 0.1666...

functionsFormulaexpand_more

Method for Terminating Decimals:

Step 1: Place the decimal over 1

2.625 = 2.625/1

Step 2: Multiply both parts by 10 for each digit after the decimal point

2.625/1 × 1000/1000 = 2625/1000

Step 3: Reduce using the Greatest Common Factor

GCF is 125 → 2625÷125 / 1000÷125 = 21/8

Step 4: Write as mixed number when applicable

21/8 = 2 5/8

Method for Repeating Decimals:

Step 1: Set x equal to your repeating decimal

x = 0.666...

Step 2: Multiply by 10 raised to the number of repeating digits

10x = 6.666...

Step 3: Subtract the first equation from the second

10x − x = 6.666... − 0.666... → 9x = 6

Step 4: Solve for x and reduce

x = 6/9 = 2/3

lightbulbExamplesexpand_more

Simple Decimal

0.625 = 5/8

From 625/1000 reduced

Decimal Greater Than 1

2.625 = 2 5/8

Same as 21/8

Single Digit Repeats

0.333... = 1/3

The 3 continues infinitely

Two Digits Repeat

0.363636... = 4/11

Pattern 36 repeats endlessly

Whole Plus Repeating

2.666... = 2 2/3

Or expressed as 8/3

Long Repeating Pattern

0.857142... = 6/7

All six digits cycle forever

quizFAQexpand_more
How should I type a repeating decimal like 0.666...?expand_more
Just type one cycle of the repeating portion (0.6) and choose how many digits repeat (1 digit in this case). The tool interprets this as 0.666... and gives you 2/3.
What if only part of my decimal repeats, like 1.8333...?expand_more
Type the number through one complete repetition (1.83), then select how many digits at the end repeat (1 digit for the 3). You'll get 1 5/6 or 11/6 as improper fraction.
Can I convert negative decimals?expand_more
Absolutely. The conversion works exactly the same way. Just convert the positive version, then put the negative sign on your fraction. So -0.75 gives you -3/4.
Is 0.9999... really equal to 1?expand_more
Yes, mathematically they're identical. Here's why: if x = 0.999..., then 10x = 9.999..., subtracting gives 9x = 9, so x = 1. It's not an approximation—they're the same number.
When do I get a mixed number versus a regular fraction?expand_more
When the numerator exceeds the denominator (like 7/4), that's called an improper fraction. A mixed number splits this into whole and fractional parts: 7/4 becomes 1 3/4.
How does simplification work?expand_more
The calculator finds the largest number that divides evenly into both numerator and denominator (the GCF), then divides both by it. For instance, 625/1000 has GCF of 125, giving 5/8.