Calcs4All

APR 23 · 2026

Decimal to fraction calculator

Convert a decimal into a simplified fraction and mixed number when applicable.

What this calculator covers

Use this calculator to rewrite a decimal as a simplified fraction without hiding the reduction steps.

Terminating decimals convert exactly, while longer decimal inputs switch to a documented best rational approximation so the result stays readable.

Frequently asked questions

When does the calculator switch from exact to approximate?
Decimals with six or fewer decimal places are converted exactly by clearing the decimal point and reducing the resulting fraction. Inputs with more than six decimal places switch to a continued-fraction search that finds the closest fraction with a denominator up to one million.
What is a mixed number and when does it appear?
A mixed number combines a whole part and a proper fraction, such as 1 3/4 instead of 7/4. The calculator shows it automatically whenever the absolute value of the input is at least one.
Can I convert negative decimals?
Yes. The sign is carried through the conversion and appears on the numerator of the resulting fraction.
How do I know if the result is exact or an approximation?
The result panel shows the conversion mode alongside the absolute error. An exact conversion will show zero error; an approximation will show a small non-zero error value.

Tool

Run the calculation

RESULT · FRACTION

â„–146

Primary result

5/4

1.25 converts to 5/4, which is 1 1/4 as a mixed number.

Simplified fraction
5/4
Mixed number
1 1/4
Conversion mode
Exact terminating-decimal conversion
Absolute error
0

Step-by-step solution

  1. 1.Start from the decimal 1.25.
  2. 2.Because the decimal terminates quickly, the calculator converts it exactly by clearing the decimal places and reducing the resulting fraction.
  3. 3.Reduce the fraction to lowest terms as 5/4 and express it as 1 1/4 when the absolute value is at least 1.

Walkthrough

Visual walkthrough

Decimal-to-fraction conversion is either exact decimal clearing or a best-fit rational search when the decimal runs long.

  1. 01

    Inspect the decimal form

    1.25

    Short terminating decimals can be converted exactly, while longer decimals may be more useful as a close rational approximation.

  2. 02

    Build the numerator and denominator

    5/4

    The calculator either clears the decimal places directly or searches continued-fraction convergents until the tolerance is met.

  3. 03

    Reduce and read the final form

    The simplified fraction is the primary result, with a mixed-number view added whenever the magnitude is at least one whole.

    5/4 = 1 1/4