Chapter 5, Problem 1CST

To determine

ToFind: The equivalent fraction of $0\cdot \overline{52}$

Answer to Problem 1CST

$\frac{52}{99}$ is the equivalent fraction of $0\cdot \overline{52}$

Explanation of Solution

Given information: Consider,the number $0\cdot \overline{52}$ provided in the question

Calculation:

To calculate the equivalent fraction of provide number, it is needed to remove bar sign.

As in the given number two digits are repeating so multiply the number by $100$

Therefore, the equivalent fraction obtained as

  $\text{let }x=\mathrm{0.5252.....}$ ………………………..(1)

  $\text{Multiply each side by }100$

Therefore,

  $100x=\mathrm{52.5252...}$ ………………………..(2)

  $\text{Subtract equation (1) from equation (2)}$

  $\begin{array}{l}\Rightarrow \left(x=\mathrm{0.5252....}\right)-\left(100x=\mathrm{52.5252....}\right)\\ \Rightarrow 100x-x=\mathrm{52.5252...}-\mathrm{0.5252...}\\ \Rightarrow 99x=52\end{array}$

  $\text{Divide each side by }99$

  $\begin{array}{l}\Rightarrow \frac{99x}{99}=\frac{52}{99}\\ \Rightarrow x=\frac{52}{99}\end{array}$

Hence,

$\frac{52}{99}$ is the equivalent fraction of $0\cdot \overline{52}$ .