Question

Which rational number equals 0.1 repeating?

Answer 1

When it has a bar over it, that means that the one continues. So the actual decimal is 0.11111111111. To find the answer, divide all the rational numbers. I'll do A for example. A. 1/11 (1 divided by 11) which is .09090909. It's close, but not the answer. Now, try the others.

The actual decimal is impossible to write out as it is infinite, so it is represented with a bar on top of the repeating value. \[0.03\]|

However the answer is 1/9

Answer 2

Answer:

0.1111.... = $\frac{1}{9}$.

Step-by-step explanation:

Given  : 0.1 repeating

To find : Which rational number equals 0.1111......

Solution : We have given 0. 11111.........

We can see there is only one number is repeating , we will multiply it by 10

Let  x = 0.1111.......

Multiply both sides by 10

10x = 10 * 0.1111.......

10x = 1.1111.......

We can write it in terms of x

10x = 1. 000 + 0.11111....

10 x = 1 + x

On subtracting both sides by x

10 x -x = 1

9 x = 1

On dividing both sides by 9

x = $\frac{1}{9}$.

0.1111.... = $\frac{1}{9}$.

Therefore, 0.1111.... = $\frac{1}{9}$.