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Byju's Answer
Standard IX
Mathematics
Irrational Numbers
Insert any tw...
Question
Insert any two irrational numbers between
4
7
and
5
7
.
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Solution
5
7
=
0.714285714285...
=
0.
¯
¯¯¯¯¯¯¯¯¯¯¯¯¯¯
¯
714285
and
4
7
=
0.571428571428...
=
0.
¯
¯¯¯¯¯¯¯¯¯¯¯¯¯¯
¯
571428
.
Here, the two decimal expansions are non-terminating recurring.
Hence,
5
7
and
4
7
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 two different irrational number between
5
7
and
4
7
can be:
0.5918264201001...
and
0.601001000100001...
NOTE:
This is two of the various possible answers. It might have different solution.
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