Question

write two different irrational numbers between the rational number 4/7 and 9\11​

Answer 1

$\huge\bf\underline{Question:}$

Write two different irrational numbers between the rational number 4/7 and 9/11.

$\huge\bf\underline{Things\:to\: Remember}$

•Rational Numbers:

These are the numbers that can be written in the form of p/q where p and q are integers and q is not equal to zero.

-There decimal expansions are terminating and if its non-terminating then the are recurring.

•Irrational Numbers:

These are the numbers that cannot be written in the form of p/q where p and q are integers and q is not equal to zero.

-There decimal expansions are non-terminating and non-recurring.

$\huge\bf\underline{Solution:}$

First,we need to divide and convert the fraction into decimals.

So,

$\frac{4}{7} =0.571428571428.... \\ \frac{9}{11} = 0.81818181.....$

Now,we need to find two irrationals between these decimals.They must be non-terminating and non-recurring.

Following are the irrationals between 4/7 and 9/11.

1)0.58558555855558......

2)0.60600600060000.....

3)0.71711711171111711111.....