Decimal to Fraction Calculator

Decimal to Fraction Calculator

Enter a decimal number, and this tool converts it to the corresponding fraction or mixed number, with detailed calculations shown.

An online decimal to fraction calculator helps you instantly convert a decimal number into its equivalent fraction and also revert repeating decimals to their original fractional form. Read on to learn about decimal fractions, conversion rules, charts, and how to convert decimal numbers into fractions effortlessly.

About Decimal Fraction:

In algebra, a decimal fraction is a fraction whose denominator is a power of 10, such as 10, 100, 1000, 10,000, and so on. Decimal fractions can be written using a decimal point, making arithmetic operations like addition, subtraction, and multiplication easier to perform.

Example of Decimal Fraction:

The fraction 7/10 is a decimal fraction. When written in decimal form, it becomes 0.7. While decimal-to-fraction conversion follows specific rules, using a decimal to fraction calculator makes the process faster and error-free.

Decimal to Fraction Chart:

A decimal to fraction chart is commonly used to convert frequently used decimal values into their equivalent fractional forms.

How to Convert Decimal to Fraction?

Decimals and fractions both represent non-integer values. To convert a decimal into a fraction, follow these steps:

Write the decimal number as a fraction by placing it over 1. For example, convert 0.65 into 0.65/1.
Multiply the numerator and denominator by 10 until the numerator becomes a whole number:

0.65 / 1 = (0.65 × 10) / (1 × 10) = 6.5 / 10

Since 6.5 is not a whole number, multiply again:

6.5 / 10 = (6.5 × 10) / (10 × 10) = 65 / 100

Simplify the fraction by dividing both numerator and denominator by their Greatest Common Factor (GCF):

(65 ÷ 5) / (100 ÷ 5) = 13 / 20

Tip: You can also use an online decimal fraction calculator for quick and accurate results.

Example:

Convert 2.625 into a fraction:

Write the decimal as a fraction:

2.625 / 1

Multiply both numerator and denominator by 1000 (since there are three decimal places):

2625 / 1000

Find the GCF of 2625 and 1000, which is 125, and simplify:

(2625 ÷ 125) / (1000 ÷ 125) = 21 / 8

Convert the improper fraction into a mixed number:

21 / 8 = 2 5 / 8

Conversion of a Negative Decimal into a Fraction:

If the decimal number is negative, first convert its absolute value into a fraction, then apply the negative sign to the final result. The decimal to fraction calculator also supports negative decimal conversions.

How to Convert a Repeating Decimal to a Fraction?

Let the repeating decimal be equal to x
Count the number of repeating digits
Multiply both sides of the equation by the appropriate power of 10
Subtract the original equation
Solve for x and simplify the fraction

Example: Convert the repeating decimal 2.666… into a fraction:

Let x = 2.666…
Multiply both sides by 10:

10x = 26.666…

Subtract the original equation:

10x − x = 26.666… − 2.666…

9x = 24

Solve for x:

x = 24 / 9 = 8 / 3

Final Answer: 2 2 / 3

About Decimal to Fraction Calculator:

An online decimal to fraction calculator instantly converts decimal numbers, including repeating decimals, into their simplest fractional form. This tool uses advanced algorithms to ensure accuracy and clarity.

How to Turn a Decimal into a Fraction Using the Calculator:

This calculator features a simple and intuitive interface that allows you to convert both terminating and repeating decimals into fractions within seconds.

Inputs:

Enter the decimal number
Specify the repeating digits (if applicable)

Outputs:

Simplified fraction
Step-by-step solution

FAQ’s (Decimal to Fraction & Repeating Decimals):

What is 0.1 as a fraction?

0.1 = 1/10

What is 0.05 as a fraction?

0.05 = 1/20

What is 0.5 as a fraction?

0.5 = 1/2

What is 0.06 repeating as a fraction?

0.06̅ = 2/33

What is 0.5 repeating as a fraction?

0.5̅ = 5/9

What is 0.15 repeating as a fraction?

0.15̅ = 5/33

What is 0.81 repeating as a fraction?

0.81̅ = 9/11

Takeaway:

This decimal to fraction calculator is designed to handle complex decimal conversions with precision. Whether you're working with terminating decimals, repeating decimals, or negative values, this tool provides quick, accurate, and step-by-step solutions.

References:

Wikipedia – Decimal Fractions
Study.com – Repeating Decimals
Math Is Fun – Decimal Fraction Definition