Question

find rational number whose absolute value is (i).9/11 (ii).4​

Answer 1

Given that,

Numbers (i) 9/11 (ii) 4

To find,

The rational numbers of the given numbers

Solution,

(i) The absolute value is 9/11. Here, numerator is 9 and denominator is 11.

To convert it into a rational number, convert the denominator and numerator with the same number. For example, we are taking 2.

So,

$\dfrac{9}{11}=\dfrac{9\times 2}{11\times 2}=\dfrac{18}{22}$

So, the rational number is 18/22 whose absolute value is 9/11.

(ii) The absolute value is 4. Here, numerator is 4 and denominator is 1.

To convert it into a rational number, convert the denominator and numerator with the same number. For example, we are taking 2.

So,

$\dfrac{4}{1}=\dfrac{4\times 2}{1\times 2}=\dfrac{8}{2}$

So, the rational number is 8/2whose absolute value is 8/2.

Answer 2

(i) The required rational number is $\pm \frac{9}{11}$ .

(ii) The required rational number is $\pm \frac{4}{1}$ .

Step-by-step explanation:

We have to find the rational number whose absolute value is (i) 9/11 and (ii)4​.

Firstly, as we know that the absolute value of a rational number '$\frac{x}{y}$' is given by;

$|\frac{x}{y} | = \frac{x}{y}$  and  $|-\frac{x}{y} | = \frac{x}{y}$

This shows whether the rational number inside the absolute brackets is positive or negative; that number will be positive only after coming out from the absolute brackets.

(i) The rational number whose absolute value is 9/11 is given by;

    $|\frac{9}{11} | = \frac{9}{11}$  and  $|-\frac{9}{11} | = \frac{9}{11}$

So, the required rational number is $\pm \frac{9}{11}$ .

(i) The rational number whose absolute value is 4 is given by;

    $|\frac{4}{1} | = \frac{4}{1}$  and  $|-\frac{4}{1} | = \frac{4}{1}$

So, the required rational number is $\pm \frac{4}{1}$ .