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Decimal Expansion of Rational and Irrational Numbers

The number 0....

Question

The number 0.318564318564318564.... is:

A

a natural number

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B

an integer

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C

a rational number

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D

an irrational number

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Solution

The correct option is C
a rational number

The number 0.318564318564318564....

= 0. $¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ 318564$

$∵$ The decimal is non-terminating and recurring

$∴$ It is rational number.

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