# How do you convert 0.bar(45) (meaning the 45 is being repeated) to a fraction?

Jun 27, 2018

$0.45454545 \ldots \ldots \ldots \ldots . = \frac{5}{11}$

#### Explanation:

Let $x = 0.45454545 \ldots \ldots \ldots \ldots .$ ............................(1)

then $100 x = 45.45454545 \ldots \ldots \ldots \ldots$ ............................(2)

subtracting (1) from (2) we get

$99 x = 45$

or $x = \frac{45}{99} = \frac{5}{11}$

Hence $0.45454545 \ldots \ldots \ldots \ldots . = \frac{5}{11}$

Jun 28, 2018

$\frac{5}{11}$

#### Explanation:

When two numbers in a decimal sequence repeat forever, the denominator will be $11$.

To think about the numerator, let's just take the number $45$.

This number would round to $50$ or $5$ tens. Whatever number of tens the numerator rounds to, this will be our numerator.

Thus, we have

$\frac{5}{11}$

Hope this helps!