Question

Write two rational numbers whose decimal form is non-terminating recurring.

Accepted Answer

We need to write two rational numbers whose decimal form is non-terminating recurring.

Consider $\frac{10}{3}$ and $\frac{9}{11}$ .

We know that $\frac{10}{3} = 10 \div 3 & \frac{9}{11} = 9 \div 11$ .

To find the decimal form of these rational numbers, we need to find the quotient of $10 \div 3 & 9 \div 11$ as follows.

$\begin{matrix} 3 & . & 3 & 3 & 3 \\ 3 & 1 & 0 \\ 9 \\ 1 & 0 \\ 9 \\ 1 & 0 \\ 9 \\ 1 & 0 \\ 9 \\ 1 \end{matrix}$

$\Rightarrow 10 \div 3 = \frac{10}{3} = 3.333 . . . .$ , which is a non-terminating recurring decimal number.

$\begin{matrix} 0 & . & 8 & 1 & 8 & 1 \\ 11 & 9 \\ 8 & 8 \\ 2 & 0 \\ 1 & 1 \\ 9 & 0 \\ 8 & 8 \\ 2 & 0 \\ 1 & 1 \\ 9 \end{matrix}$

$\Rightarrow 9 \div 11 = \frac{9}{11} = 0.8181 . . . . . . . .$ , which is a non-terminating recurring decimal number.

Thus, we obtained two rational numbers $\frac{10}{3} & \frac{9}{11}$ whose decimal form is non-terminating recurring.

Chhattisgarh Board Solutions for Exercise 9: Try This

Chhattisgarh Board Mathematics Solutions for Exercise - Chhattisgarh Board Solutions for Exercise 9: Try This

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