What is 0.4 repeating as a fraction?

Fractions are very important concepts that are used in advanced mathematics topics as well. The repeating or recurring fractions are those which have an infinite number of decimal places following a pattern.

Answer: 0.4 repeating as a fraction can be written as 4/9 in fractions.

Let's understand the solution in detail.

Explanation:

0.4 repeating is a recurring fraction with infinite decimal places.

To convert it into fractions, we follow the below steps:

First, we can write:

x = 0.4 repeating = 0.444... (1)

Now, we multiply both sides by 10:

⇒ 10x = 4.444... (2)

Subtracting (1) from (2), we get:

⇒ 10x − x = 4.444... - 0.444...

We can now solve for x as follows:

⇒10x − x = (4 + 0.444...) − 0.444...

⇒ (10 − 1) x = 4 + 0

⇒ 9x = 4

⇒x = 4/9

Hence, 0.4 repeating can be written as 4/9 in fractions.