Decimal to Fraction Calculator

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

Related

Decimal to Fraction Calculator

An online decimal to fraction calculator helps you instantly convert decimal numbers into their equivalent fractions, including repeating decimals. It also provides step-by-step guidance for accuracy.

About Decimal Fraction

A decimal fraction is a fraction whose denominator is a power of 10 (10, 100, 1000, etc.). Decimal fractions are written using a decimal point, which simplifies arithmetic operations like addition, subtraction, and multiplication.

Example:

The fraction 7/10 is a decimal fraction. Written in decimal form: 0.7.

Decimal to Fraction Chart:

Common decimals can be quickly converted using a chart that maps decimal values to their fractional equivalents.

How to Convert Decimal to Fraction

Follow these steps to convert a decimal into a fraction:

Write the decimal over 1. Example: 0.65 → 0.65/1

Multiply numerator and denominator by 10 until the numerator becomes a whole number:

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

Example: Convert 2.625 into a Fraction

Write as a fraction: 2.625 / 1
Multiply numerator and denominator by 1000 (three decimal places): 2625 / 1000
Find GCF = 125 and simplify: (2625 ÷ 125) / (1000 ÷ 125) = 21 / 8
Convert to a mixed number: 21 / 8 = 2 5 / 8

Negative Decimal Conversion

Convert the absolute value first, then apply the negative sign. The calculator supports negative decimals.

Converting Repeating Decimals to Fractions

Let the repeating decimal = x
Count the repeating digits and multiply both sides by the appropriate power of 10
Subtract the original equation and solve for x

Example: Convert 2.666… to Fraction

x = 2.666…
10x = 26.666…
10x - x = 26.666… - 2.666…
9x = 24
x = 24 / 9 = 8 / 3
Final Answer: 2 2 / 3

About the Decimal to Fraction Calculator

This tool converts decimals, including repeating decimals, into their simplest fractional form. It provides step-by-step solutions for clarity and accuracy.