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Decimal Expansion of Rational and Irrational Numbers

Explain, how ...

Question

Explain, how irrational number differ from rational numbers ?

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Solution

A rational number can be expressed in either terminating decimal or non-terminating recurring decimals but an irrational number is expressed in non-terminating non-recurring decimals.

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Q. Give an example of each, of two irrational numbers whose:
(i) difference is a rational number.
(ii) difference is an irrational number.
(iii) sum is a rational number.
(iv) sum is an irrational number.
(v) product is an rational number.
(vi) product is an irrational number.
(vii) quotient is a rational number.
(viii) quotient is an irrational number.

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