How-to guides · 3 min read

How to Convert a Decimal to a Fraction (Including Repeating)

Published October 3, 2026Written and reviewed by Mateuss M.

In short: Write the decimal over a power of ten and simplify: 0.375 = 375/1000 = 3/8. Repeating decimals need one extra algebra step.

Terminating decimals

Count the digits after the point. One digit → over 10, two → over 100, three → over 1000. Then reduce with the greatest common factor.

0.375 as a fraction

Answer3/8

Decimal: 0.375
Check: 3 × 125 = 375 and 8 × 125 = 1000

Step-by-step working 3 steps

1
Write the fraction
```
375/1000
```
2
Find the greatest common factor (Euclid’s algorithm)
```
375 = 0 × 1000 + 375
1000 = 2 × 375 + 250
375 = 1 × 250 + 125
250 = 2 × 125 + 0
```
Divide repeatedly, keeping the remainder, until the remainder is 0. The last non-zero remainder is the GCF: 125.
3
Divide top and bottom by the GCF
```
375 ÷ 125 = 3
1000 ÷ 125 = 8
→ 3/8
```

Another: 0.6 = 6/10 = 3/5, and 0.04 = 4/100 = 1/25.

Decimals with a whole part

3.25 = 3 + 25/100 = 3 + 1/4 = 3 1/4, or as an improper fraction 13/4.

Repeating decimals: the algebra trick

Let x = 0.333…. Multiply by 10: 10x = 3.333…. Subtract: 9x = 3, so x = 3/9 = 1/3. For 0.727272…: let x = that, 100x = 72.7272…, so 99x = 72 and x = 72/99 = 8/11.

0.7272… as a fraction

Answer8/11

Decimal: 0.727273
Check: 8 × 9 = 72 and 11 × 9 = 99

Step-by-step working 3 steps

1
Write the fraction
```
72/99
```
2
Find the greatest common factor (Euclid’s algorithm)
```
72 = 0 × 99 + 72
99 = 1 × 72 + 27
72 = 2 × 27 + 18
27 = 1 × 18 + 9
18 = 2 × 9 + 0
```
Divide repeatedly, keeping the remainder, until the remainder is 0. The last non-zero remainder is the GCF: 9.
3
Divide top and bottom by the GCF
```
72 ÷ 9 = 8
99 ÷ 9 = 11
→ 8/11
```

Check your answer

Divide back: 3/8 = 0.375. The fraction calculator also accepts decimals directly and shows the fraction it makes.

Frequently asked questions

What is 0.5 as a fraction?

5/10 = 1/2.

How do I convert 0.125 to a fraction?

125/1000 = 1/8.

Written and reviewed by Mateuss M.

Mateuss M. writes and reviews mathematical content for CalcSolver, focusing on online calculators, formulas, equations, and practical math tools. He reviews calculator functionality, calculation methods, formulas, examples, and explanations to help ensure that each tool is clear, useful, and easy to understand.

Keep reading

How-to guides

How to Convert a Decimal to a Fraction (Including Repeating)

Terminating decimals

Decimals with a whole part

Repeating decimals: the algebra trick

Check your answer

Frequently asked questions

Written and reviewed by Mateuss M.

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