Question

express 0.34 bar 34 in p/q form ​

Answer 1

$0.\overline{34}$ can be expressed as $\dfrac{34}{99}$

Step-by-step explanation:

• Here, the given number is $0.\overline{34}$. We have to express this number in the form $\dfrac{p}{q}$, where $p,q\in\mathbb{Z}$ and $q\neq 0$.

Let, $x=0.\overline{34}$

$\Rightarrow x=0.34343434...$

Multiplying both sides by $100$, we get

$\quad 100x=34.34343434...$

Now, $100x-x=34.3434...-0.343434...$

$\Rightarrow 99x=34$

$\Rightarrow \boxed{x=\dfrac{34}{99}}$

Thus we can express $0.\overline{34}$ in the form $\dfrac{p}{q}$ as $\dfrac{34}{99}$, a rational number.