What is .5 repeating as a fraction?

Fractions are a very important concept that is 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: 0.5 repeating as a fraction can be written as 5/9.

Let's understand the solution in detail.

Explanation:

0.5 repeating is a recurring fraction with infinite decimal places.

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

First, we can write:

⇒ x = 0.5 repeating = 0.555... (1)

Now, we multiply both sides by 10:

⇒ 10x = 5.555... (2)

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

⇒10x − x = 5.555... - 0.555...

We can now solve for x as follows:

⇒10x − 1x=(5 + 0.555...) − 0.555...

⇒(10 − 1) x = 5 + 0

⇒9x = 5 

⇒x = 5/9

Hence, 0.5 repeating can be written as 5/9 in a fraction.