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Find three different irrational numbers between the rational n

Question

Find three different irrational numbers between the rational numbers $\frac{5}{7}$ and $\frac{9}{11}$ .

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Find three different irrational numbers between the rational numbers

\frac{5}{7}

and

\frac{9}{11}

10 mins ago

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10 mins ago

Text solutionVerified

\frac{5}{7} = 0.714285714285... = 0. \overline{714285}

and

\frac{9}{11} = 0.8181... = 0. \overline{81}

Here, the two decimal expansions are non-terminating recurring.

Hence,

\frac{5}{7}

and

\frac{9}{11}

are two rational numbers.

We know, between any two rational numbers, there are infinitely many irrational numbers.

An irrational number has non-terminating non-recurring decimal expansions.

Then three different irrational number between

\frac{5}{7}

and

\frac{9}{11}

can be:

0.750750075000075...

0.767076700767...

0.808008000800008...

NOTE:

This is three of the various possible answers. It might have different solution.

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Question Text	Find three different irrational numbers between the rational numbers $\frac{5}{7}$ and $\frac{9}{11}$ .
Answer Type	Text solution:1
Upvotes	151