Convert Decimal to Fractions!

Convert any decimal number to fraction.

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How to use the Decimal to Fraction Calculator?

Calculator features

🔢 Result Format:	Reduced fraction or Mixed number
⚡ Speed of Computation:	Instant!
➡️ Calculator Output:	Display, Copy, Save
🎯 Calculator Accuracy:	100%
📋 Definitions and Formulas:	Available

What is a Decimal number?

In math, a decimal numeral denotes a non-integer number; in other words, a number that shows a decimal point followed by digits to represent the fractional part.

Decimal numbers are an alternative way to express fractions, in which the digits to the left of the decimal point represents the integer or whole number, and the digits to the right of the decimal point represent the decimal fractions.

Examples of decimal numbers:

0.1, which equals to 1/10

2.5, which equals to 2 + 1/2

How to convert Decimal to Fraction

The goal of converting a decimal to fraction is to find two integer numbers (one numerator and one denominator) which we can divide by themselves to get the initial value.

This is the general process to convert a decimal to fraction:

1. Write the decimal as the numerator (the top number of the fraction) and 1 as the denominator (the bottom number of the fraction, also known as the tenths place).
2. Multiply both the numerator and the denominator by 10, as many times as the number of decimal places (the digits after the decimal point)
3. Simplify / reduce the fraction: rewrite the fraction in its simplest form:
   1. Find the Greatest Common Divisor (GCD) between the numerator and the denominator
   2. Divide both the numerator and the denominator by the GCD

Example:

Let’s convert 4.125 to Fraction. Write the fraction as 4 0.125 / 1

Now multiply both the numerator and the denominator by 10, for 3 times (since 0.125 has 3 decimal digits): 4 125 / 1000

The GCD between 125 and 1000 is 125, so divide both the numerator and the denominator of the fraction 125/1000 by 125 to simplify the fraction to 4 1/8

How to convert a Negative Decimal to Fraction

If the decimal is negative, the process is the same, but the fraction will have a negative sign in front of itself.

Example: let’s convert -2.5 to fraction. Write the fraction as -2 5/10

The GCD between 5 and 10 is 5, so divide both the numerator and the denominator of the fraction -5/10 by 5 to simplify the fraction to -2 1/2

How to convert Repeating Decimals to Fraction

You may encounter repeating decimal digits, such as 0.3333333… (which is often represented as 0.3, where the line over the decimal 3 means that it is repeated).

In this case the conversion involves solving equations:

1. Let the decimal number be “x” in the equation
2. Count the number of repeating decimal digits, and let be “y”
3. Multiply both sides of the equation by 10^y
4. Subtract the initial equation from the resulting equation
5. Solve for x
6. Simplify the fraction

Example: let’s convert 0.13 to fraction.

The equation will be x = 0.13

Multiply both sides by 10¹ (since there is one repeating decimal): 10x = 1.3

Now subtract the initial equation from the resulting equation: (10x – x) = (1.3 – 0.13)

The result is 9x = 1.2

Solve the equation: x = 1.2 / 9

Multiply both the numerator and the denominator by powers of 10 to eliminate the decimal places on the numerator: 12 / 90

Simplify the fraction by finding the GCD for both 12 and 90 (which is 6) and divide both values by 6.

The result is 2/15

Common Decimals to Fraction conversion table

Decimal	Fraction
0.00001	1/100000
0.0001	1/10000
0.001	1/1000
0.01	1/100
0.08333333	1/12
0.09090909	1/11
0.1	1/10
0.11111111	1/9
0.125	1/8
0.14285714	1/7
0.16666667	1/6
0.2	1/5
0.22222222	2/9
0.25	1/4
0.28571429	2/7
0.3	3/10
0.33333333	1/3
0.375	3/8
0.4	2/5
0.42857143	3/7
0.44444444	4/9
0.5	1/2
0.55555555	5/9
0.57142858	4/7
0.6	3/5
0.625	5/8
0.66666667	2/3
0.7	7/10
0.71428571	5/7
0.75	3/4
0.77777778	7/9
0.8	4/5
0.83333333	5/6
0.85714286	6/7
0.875	7/8
0.88888889	8/9
0.9	9/10
1.1	11/10
1.2	6/5
1.25	5/4
1.3	13/10
1.4	7/5
1.5	3/2
1.6	8/5
1.7	17/10
1.75	7/4
1.8	9/5
1.9	19/10
2.5	5/2