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Find three rational and irrational number between -2 and -3

Posted by Aashika Bi 2 years, 3 months ago

CBSE > Class 09 > Mathematics

1 answers

Preeti Dabral 2 years, 3 months ago

Since we know that rational number between two rational numbers is obtained by $\frac{1}{2}$ [a+b]
A rational number lying between -2 and -3 is $\frac{1}{2}$ [(-2) + (-3)],
i.e., $-\frac{5}{2}$
Now, a rational number lying between -2 and $-\frac{5}{2}$ is
$\left.\frac{1}{2}[(-2)+\left(-\frac{5}{2}\right)\right ]$
= $\frac{1}{2} \times\left(-\frac{9}{2}\right)$
= $-\frac{9}{4}$
And, a rational number lying between $-\frac{5}{2}$ and -3 is
$\frac{1}{2}\left(\left(-\frac{5}{2}\right)+(-3)\right)$
$\frac{1}{2} \times\left(-\frac{11}{2}\right)$
$-\frac{11}{4}$
Thus, we have $-2>-\frac{9}{4}>-\frac{5}{2}>-\frac{11}{4}>3$
Hence, three rational numbers between -2 and -3 are $-\frac{9}{4},-\frac{5}{2}$ and $-\frac{11}{4}$

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CBSE > Class 09 > Mathematics