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Which of the following irrational number lies between $2.5$ and $2.6$ ?

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2.512

2.77321

2.5333 . . .

2.5135145 . . .

answer is D.

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Detailed Solution

Given range is

2.5

2.6

and the options

2.512

2.77321

2.5333 . . .

and

2.5135145 . . .

2.512

and

2.77321

are rational numbers as the decimal expansion terminates.

2.5333 . . .

can be rewritten as

2.5 \underset{̲}{3}

, which is also a rational number, as it is non-terminating recurring.
But

2.5135145 . . .

is non-terminating non-recurring and therefore is an irrational number and lies between

2.5

and

2.6

.
Therefore, option (4) is correct.

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