How do you convert $0.19$ ( $19$ repeating) to fraction?

Open in App

Solution

Solve for the required fraction:
Given that $0.19$ ( $19$ repeating)
Let $x = 0.1919191919 . . . . . . . . .,$
$\Rightarrow$ $100 x = 19.1919191919 . . . . .$
Subtracting former from latter we get
$99 x = 19$
$\Rightarrow$ $x = \frac{19}{99}$
Thus $0.1919191919 . . . . = \frac{19}{99}$ .
Hence, the required fraction is $\frac{19}{99} .$

Suggest Corrections

Similar questions

.63

How do you convert $0.87$ $(7$ repeating $)$ to a fraction?

How do you convert $0.36$ ( $36$ repeating) to a fraction?

Join BYJU'S Learning Program