Which of the following is a rational number and an irrational number that lie between $− 2 5 and 12$ ?

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A rational number 0 and an irrational number 0.151151115….

A rational number 1 and an irrational number 0.080030003….

A rational number 0.151151115…. and an irrational number -0.050050005..

None of the above

answer is A.

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Detailed Solution

It is given that we have to find a rational number between

− 2 5 and 12

i.e., between – 0.4 and 0.5.
A rational number is of the form

p q,

where p and q are integers and

q ≠ 0

, otherwise, it is an irrational number.
We know that there is an infinite number of rational and irrational values between any two numbers.
A rational number between

− 2 5 and 12

i.e., between – 0.4 and 0.5 is 0.
To find an irrational number between

− 2 5 and 12

, it should be a non-terminating, non-recurring number lying between them.
Therefore, such numbers will be 0.151151115…
Therefore, the correct answer is a rational number 0 and an irrational number is 0.151151115….
Therefore, the correct option is (1).

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