# What Is 0.4 Repeating As a Fraction?

0.4 repeating as a fraction is equal to 4/10. The decimal 0.4 repeating means that the 4 goes on infinitely after the decimal point.

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## What is a repeating decimal?

A repeating decimal is a decimal number whose digits are periodic (i.e., they repeat themselves indefinitely). The decimal 0.4 repeating, therefore, consists of the digits 4, followed by an infinite repetition of the digits 0.

## What is 0.4 repeating as a fraction?

To convert 0.4 repeating to a fraction, we need to find the number that when multiplied by 10 would give us 4 with a remainder of 0. In other words, we’re looking for a number x such that:

10x = 4 (mod 9)

Since 9 is a prime number, we can use Fermat’s little theorem to simplify this equation:

10x = 4 (mod 9)
10x = 40 (mod 9)
x = 40/9 (mod 9)

Since 40/9 is equal to 4 2/3, the fractional form of 0.4 repeating is 4 2/3.

## How can you convert a repeating decimal to a fraction?

There are a few steps you can follow to convert a repeating decimal to a fraction. In general, you will need to determine the decimal’s repeating pattern, and then express that pattern as a fraction. To do this, you will need to use some basic division.

Here is an example of how to convert 0.4 repeating to a fraction:

First, you will need to determine the decimal’s repeating pattern. In this case, the repeating pattern is “0.4.”

Next, you will need to express that pattern as a fraction. To do this, you can divide 1 by the number that the decimal repeats (in this case, 4). This gives you the fraction 1/4.

Finally, you can simplify the fraction if desired. In this case, 1/4 is already in its simplest form.

Thus, 0.4 repeating can be expressed as the fraction 1/4.

## What are some other examples of repeating decimals?

Other repeating decimals include 1/11=0.090909…, 2/16=0.125, and 1/90=0.01111…. You can also have repeating decimals where the decimal expansion doesn’t start right away. For example, 1/6=0.16666…. has a repeating decimal expansion, but it doesn’t start until the 6.