Question

11. Find 6 rational numbers between
-5/7 and -2/3​

Answer 1

Answer :-

The six rational number between -5/7 and -2/3​ are

1. -0.6905

2. -0.6787

3. -0.7022

4. -0.69635

5. -0.67285

6. -0.69045.

Solution :-

• Formula to find rational number between any given integers is -

$\boxed{\longrightarrow \dfrac{1}{2} [a+b]}$

where,

a = first integer

b = second integer

Note:- As the number of rational numbers to find increases, the value of a or b changes. The value of a or b that changes are the same rational number founded between them.

‣ First rational number

$a = \dfrac{-5}{7} =-0.714\\\\b=\dfrac{-2}{3}=-0.667$

$\longrightarrow \dfrac{1}{2} \left[-0.714+(-0.667)\right]\\ \\ \longrightarrow \dfrac{1}{2} \left[-1.381\right]\\ \\ \longrightarrow -0.6905$

‣ Second rational number

Now,

$a =- 0.6904\\\\b=-0.667$

$\longrightarrow \dfrac{1}{2} \left[-0.6904+(-0.667)\right]\\ \\ \longrightarrow \dfrac{1}{2} \left[-1.374\right]\\ \\ \longrightarrow -0.6787$

‣ Third rational number

Now,

$a =-0.714 \\\\b=-0.6904$

$\longrightarrow \dfrac{1}{2} \left[-0.714+(-0.6904)\right]\\ \\ \longrightarrow \dfrac{1}{2} \left[-1.4044\right]\\ \\ \longrightarrow -0.7022$

‣ Fourth rational number

$a =-0.714 \\\\b=-0.6787$

$\longrightarrow \dfrac{1}{2} \left[-0.714+(-0.6787)\right]\\ \\ \longrightarrow \dfrac{1}{2} \left[-1.3927\right]\\ \\ \longrightarrow -0.69635$

‣ Fifth rational number

$a =-0.6787 \\\\b=-0.667$

$\longrightarrow \dfrac{1}{2} \left[-0.6787+(-0.667)\right]\\ \\ \longrightarrow \dfrac{1}{2} \left[-1.3457\right]\\ \\ \longrightarrow -0.67285$

‣ Sixth rational number

$a =-0.7022 \\\\b=-0.6787$

$\longrightarrow \dfrac{1}{2} \left[-0.7022+(-0.6787)\right]\\ \\ \longrightarrow \dfrac{1}{2} \left[-1.3809\right]\\ \\ \longrightarrow -0.69045$

Therefore, the six rational number between -5/7 and -2/3​ are -0.6905, -0.6787, -0.7022, -0.69635, -0.67285 and -0.69045.