Chapter 5.1, Problem 5C

To determine

To find: The fraction form of $0.3$ and $0.\overline{3}$ and compare both.

Answer to Problem 5C

The fraction form of $0.3$ and $0.\overline{3}$ are $\frac{3}{10}$ and $\frac{1}{3}$ respectively also fraction $\frac{1}{3}$ is greater than the fraction $\frac{3}{10}$ .

Explanation of Solution

Given information: Consider the number $0.3$ and $0.\overline{3}$ as provided in the question

As provided number $0.3$ is a terminating number and having 3 at tenth place

Therefore, the fraction form obtained as:

  $\Rightarrow 0.3=\frac{3}{10}$

Also the provided number $0.\overline{3}$ is a repeating number and repeat one digit 3

Let $x=\mathrm{0.333....}$ equation $(1)$

Here one digit is repeating so multiply each side by $10$

  $\Rightarrow 10x=\mathrm{3.333....}$ equation $(2)$

subtract equation $(2)$ from equation $(1)$

  $\begin{array}{l}\Rightarrow 10x-x=\mathrm{3.333....}-\mathrm{.333....}\\ \Rightarrow 9x=3\\ \Rightarrow x=\frac{3}{9}\\ \Rightarrow x=\frac{1}{3}\end{array}$

Also, $\mathrm{0.333...}>0.300$

Therefore, fraction $\frac{1}{3}$ is greater than the fraction $\frac{3}{10}$

Conclusion:

The fraction form of $0.3$ and $0.\overline{3}$ are $\frac{3}{10}$ and $\frac{1}{3}$ respectively also fraction $\frac{1}{3}$ is greater than the fraction $\frac{3}{10}$ .