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Q.

Write one rational and one irrational number lying between 0.25 and 0.32.


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a

Rational number is 0.28 and Irrational number is 0.280280028000….

b

Rational number is 1.28 and Irrational number is 1.280280028000….

c

Rational number is 2.28 and Irrational number is 2.280280028000….

d

Rational number is 3.28 and Irrational number is 3.280280028000…. 

answer is A.

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Detailed Solution

We know that, a number which cannot be expressed in the form p/q, where p,q are integers, and q ≠ 0, is called an irrational number.
These numbers neither terminates nor repeat the particular number in the process of division. So, it is said to be a non-terminating non-repeating decimal expansion.
Also, we know that a number which can be expressed as p/q, where p,q are integers, and q ≠ 0, is called a rational number.
Rational numbers have terminating or non-terminating, repeating decimal expansion.
We need to find one rational and one irrational number lying between 0.25 and 0.32.
By applying the concept of rational numbers,
the number 0.28 lies between 0.25 and 0.32 and can be represented as 28/100.
So, it is a rational number.
By applying the concept of irrational numbers,
The number 0.280280028000…. lies between 0.25 and 0.32 and cannot be represented in the form of p/q.
So, it is an irrational number.
Hence, one rational and one irrational number lying between 0.25 and 0.32 is 0.28 and 0.280280028000…..
The correct option is (1).
 
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