Question

HELLO !!


QUESTION ;

FIND A IRRATIONAL NO BETWEEN :

1/7 & 2/7


NOTE :

NO SPAMMING ❌
NO DIRECT ANSWERS ❌
NO GUESSING ❌
KINDLY SHOW WORKOUT ✅


SUBJECT :

MATH'S



THANKS ! ​

Answer 1

Answer:

$\frac{1}{7}$ = 0.142857 bar

and,

$\frac{2}{7}$ = 0.285714 bar

So, Two irrational numbers are

0.175010010001...

0. 194010010001....

Answer 2

Question :-

Find an Irrational Number between $\mathtt{\dfrac{1}{7}}$ and $\mathtt{\dfrac{2}{7}}$.

$\begin{gathered} \end{gathered}$

Solution :-

By Actual Division, we know that $\mathtt{\dfrac{1}{7} = 0.\overline{142857}}$ and $\mathtt{\dfrac{2}{7} = 0.\overline{285714}}$ .

$\begin{gathered} \end{gathered}$

To find an Irrational Number between $\mathtt{\dfrac{1}{7}}$ and $\mathtt{\dfrac{2}{7}}$, we find a Number which is Non-Terminating, Non-Recurring lying between them.

$\begin{gathered} \end{gathered}$

An example of such a Number is 0.25025002500025... $\red{\star}$

$\bullet$ There are infinitely many Irrational Numbers between any two Irrational Numbers.

$\begin{gathered} \end{gathered}$

Additional Information :-

Irrational Numbers :-

A Number which can neither be Expressed as a Terminating nor as a Repeating Decimal, is called an Irrational Number.

$\begin{gathered} \end{gathered}$

Thus, Non-terminating, Non-repeating Decimals are Irrational Numbers.