Question

(checking answer!) What is the fraction representation of 0.196 (6 repeating)?

Answer 1

Answer:

49/250 I think I'm not sure though

Answer 2

Answer:

$\frac{59}{300}$

Step-by-step explanation:

Recall that $\frac{x}{9}$ returns the decimal $0.\overline{x}$. In this case, we only want the 6 repeating. We can achieve this by finding the fraction excluding the 6 and then adding the repeating fraction with the 6.

0.19 as a fraction is simply $\frac{19}{100}$

$\frac{6}{9}$ returns a repeating digit 6. However, we would like the 6 to be in the thousands place. Since it's already in the tenth place, we will divide the fraction by 100 to put it in the thousands place: $\frac{6}{9}\cdot \frac{1}{100}=\frac{6}{900}$

Adding these two fractions, we get:

$\frac{6}{900}+\frac{19}{100}=\frac{6}{900}+\frac{171}{900}=\frac{177}{900}=\boxed{\frac{59}{300}}$