What is 0.15 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: 0.15 repeating as a fraction can be written as 5/33 in a fraction.

Let's understand the solution in detail.

Explanation:

0.15 repeating is a recurring fraction with infinite decimal places.

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

First, we can write:

x = 0.15 repeating = 0.1515... (1)

Now, we multiply both sides by 100:

⇒ 100x = 15.1515... (2)

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

⇒ 100x − x = 15.1515... - 0.1515...

We can now solve for x as follows:

⇒ 100x − x = (15 + 0.1515...) − 0.1515...

⇒ (100 − 1) x = 15 + 0

⇒ 99 x = 15

After simplifying the fraction:

⇒ x = 15/99 = 5/33

Hence, 0.15 repeating can be written as 5/33 into fractions.