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.