Question

$3.7777...$when expressed in the form of $\frac{p}{q}\text{is}........$

Answer 1

Expressing $3.77\dots \dots \dots$ in $\frac{p}{q}$ form:

Given irrational number is $3.77\dots \dots \dots$

Now,

We have to express $3.77\dots \dots \dots$ in the form of $\frac{p}{q}$.

Let us assume that $x=$ $3.77\dots \dots \dots$ (1)

Now, multiply by $10$ on both sides, we get

$10x=$ $37.77\dots \dots \dots$ (2)

Now, subtract $\left(1\right)\text{from}\left(2\right)$, we get

$$\begin{gathered} 10x-x=34 \\ 9x=34 \\ x=\frac{34}{9} \end{gathered}$$

Hence, $3.7777...$ can be expressed in the form $\frac{p}{q}$ is…..$\frac{34}{9}$