Repeating Decimal to Fraction Calculator

Now you can perform your calculations even faster by using the Repeating Decimal and Fraction Calculator. The simple tool allows the user to enter a repeating decimal as an input box and, with a click of the Calculate button, it creates the output result in its original fraction form in a fraction of a second.

Enter Non-Repeating Part After Decimal
Enter Repeating Part After Decimal

Repeating Decimal to Fraction Calculator: This Repeating Decimal to Fraction Calculator is a one-stop solution for your problem. If you are looking for an acceptable tool that computes repeating decimal and delivers the available fractional values. Examine the step-by-step technique and the simplest way for solving Repeating Decimal issues, as well as the notion of Fractions from the further modules.

What are Repeating Decimals and Fractions?

Repeating Decimals:

It is a periodic representation of numbers and the repeated portion is non-zero. A number will be rational when its decimal representation is terminating or repeating.

Fractions:

Fractions are the numbers that are represented as a quotient, which includes a numerator and a denominator. It is of three types i. e simple fraction:- both numerator and denominator are integers.

Proper fraction:- The numerator is less than that of the denominator.

Improper fraction:- The numerator is more than that of the denominator.

This module has both step-by-step instructions as well as an online calculator that provides correct results in a relatively short period of time. Visit arithmeticcalculator.com to discover a variety of useful calculators and complete your calculations with ease.

Steps to perform the Repeating Decimal to Fraction Conversion Manually

Step 1:Let X be the repeating decimal that you want to convert into a fraction.

Step 2:Then you have to examine the repeating decimal for finding the repeating digits.

Step 3:Then repeating digits should be placed at the left of the decimal point.

Step 4:Then you have to place the repeating digits to the right of the decimal point.

Step 5:Using the equations of step 3 and step 4, You have to subtract the left sides of these two equations, and also you have to subtract the right sides of these two equations.

Subtraction should be such that the difference is positive for both sides.

Solved Example of Repeating Decimal to Fraction Conversion with Steps

Example:

Convert the following to a fraction: 0.4280611

non-repeating part: 428

repeating part: 0611

Solution:

Given that,

non-repeating part: 428 and repeating part: 0611

Thus, solving for fraction,

=428/1000

=(0611/9999)/1000 = 0611/9999000

=428/1000+0611/9999000

=4280183/9999000

FAQs On Free Online Repeating Decimal Calculator with Steps

1. What is the rule for repeating decimals?

The rule for repeating decimals says that the period of a repeating decimal must be written first in the numerator of an ordinary fraction, while the denominator must contain some number of nines.

In such a case, the number of nines should be equal to the number of digits in the period of the repeating decimal 0.

2. Why do some decimals repeat?

While dividing the numerator with the denominator if it ends up with a remainder 0 then we get a terminating decimal but if it does not end up with a remainder 0 then the remainders will begin to repeat after some point as a result, we get a repeating decimal.

3. Why do some fractions repeat?

Some fractions repeat if the prime factorization of the denominator of a fraction is any prime factor in the denominator other than 2 or 5, then the decimal expression repeats, as the expression, in this case, does not get terminated.