Decimal to Fraction Calculator

Decimal Number:

Trailing Decimals:

Using the Calculator

This tool helps you change decimal numbers to fractions or mixed numbers easily. For decimals that repeat, you have to tell the calculator how many digits repeat.

Inputting Repeating Decimals

If you have a decimal like 0.66666… where the digit 6 keeps going, enter 0.6. Then, input 1 for the repeating places. The fraction you get is 2/3.
When you have a decimal like 0.363636… where 36 repeats, enter 0.36. Next, input 2 for the places because ’36’ are the repeating numbers. The answer will be 4/11.
For a decimal like 1.8333… where only 3 repeats, enter 1.83 and input 1 for the repeating spot. The mixed number is 1 5/6.
For a longer repeating decimal like 0.857142857142… where 857142 repeats, enter 0.857142. Then, put in 6 for repeating places because 857142 are the numbers repeating. The result is 6/7.

These steps guide you in using the calculator to handle different decimals accurately and get correct fractions or mixed numbers.

Changing a Negative Decimal to a Fraction

Remove the negative sign from your decimal number.
Convert the positive decimal to a fraction.
Add the negative sign back to your fraction.

Steps to Change a Decimal into a Fraction

Example: Converting 2.625 into a Fraction

Begin by expressing 2.625 as a fraction by placing it over 1:
$\frac{2.625}{1}$
To remove the decimal, multiply both the numerator and the denominator by 1000 to account for the three decimal places:
$\frac{2.625 \times 1000}{1 \times 1000} = \frac{2625}{1000}$
Next, find the Greatest Common Factor (GCF) of 2625 and 1000, which is 125. Then, divide both by their GCF to simplify:
$\frac{2625 \div 125}{1000 \div 125} = \frac{21}{8}$
Transform the simplified fraction into a mixed number:
$2 \frac{5}{8}$

So, 2.625 changes to $2 \frac{5}{8}$ as a fraction.

Turn a Repeating Decimal into a Fraction

Example: Transform the Repeating Number 2.666 into a Fraction

Begin by setting up an equation: Let ( x ) equal the number, so you have:

[x = 2.\overline{666} ]

2. Identify the decimal places: There are 3 digits repeating, so let ( y = 3 ). Multiply both sides of the initial equation by ( 10^3 = 1000 ):

1000x = 2666.\overline{666}

3. Subtract the two equations:

[ \begin{aligned} 1000x &= 2666.\overline{666} \\ x &= 2.\overline{666} \\ \hline 999x &= 2664 \end{aligned} ]

4. Solve for ( x ):

x = \frac{2664}{999}

5. Simply the fraction: Determine the greatest common factor (GCF) of 2664 and 999, which is 333. Divide both the numerator and denominator by the GCF:

\frac{2664 \div 333}{999 \div 333} = \frac{8}{3}

The simplified improper fraction is then:

= 2 \frac{2}{3}