Question

Find six national numbers between 3 and 4​

Answer 1

$\underline{\textbf{Given:}}$

$\textsf{Numbers are 3 and 4}$

$\underline{\textbf{To find:}}$

$\textsf{Six rational numbers between 3 and 4}$

$\underline{\textbf{Solution:}}$

$\textsf{We apply Average method to find rational numbers between 3 and 4}$

$\mathsf{Average\;of\;3\;and \;4}$

$\mathsf{=\dfrac{3+4}{2}}$

$\mathsf{=\dfrac{7}{2}}$

$\implies\boxed{\mathsf{c_1=\dfrac{7}{2}}}$

$\mathsf{Average\;of\;3\;and \;\dfrac{7}{2}}$

$\mathsf{=\dfrac{3+\dfrac{7}{2}}{2}}$

$\mathsf{=\dfrac{\dfrac{13}{2}}{2}}$

$\implies\boxed{\mathsf{c_2=\dfrac{13}{4}}}$

$\mathsf{Average\;of\;3\;and \;\dfrac{13}{4}}$

$\mathsf{=\dfrac{3+\dfrac{13}{4}}{2}}$

$\mathsf{=\dfrac{\dfrac{25}{4}}{2}}$

$\implies\boxed{\mathsf{c_3=\dfrac{25}{8}}}$

$\mathsf{Average\;of\;3\;and \;\dfrac{25}{8}}$

$\mathsf{=\dfrac{3+\dfrac{25}{8}}{2}}$

$\mathsf{=\dfrac{\dfrac{49}{8}}{2}}$

$\implies\boxed{\mathsf{c_4=\dfrac{49}{16}}}$

$\mathsf{Average\;of\;3\;and \;\dfrac{49}{16}}$

$\mathsf{=\dfrac{3+\dfrac{49}{16}}{2}}$

$\mathsf{=\dfrac{\dfrac{97}{16}}{2}}$

$\implies\boxed{\mathsf{c_5=\dfrac{97}{32}}}$

$\mathsf{Average\;of\;3\;and \;\dfrac{97}{32}}$

$\mathsf{=\dfrac{3+\dfrac{97}{32}}{2}}$

$\mathsf{=\dfrac{\dfrac{193}{32}}{2}}$

$\implies\boxed{\mathsf{c_6=\dfrac{193}{64}}}$

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Answer 2

Given :   number 3 and 4

To Find : 6 rational numbers in between

Solution:

3  = 30/10

4 = 40/10

Rational number between

31/10 , 32/10  , 33/10 , 34/10 , 35/10  , 36/10 , 37/10 , 38/10 , 39/10

31/10  , 16/5  , 33/10  , 17/5  , 7/2 , 18/5  , 37/10 , 19/5  , 39/10

There exist infinite rational number between any two distinct real numbers

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