Classify 7.478478... as rational or irrational.

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Rational

Irrational

Both of these

None of the above

answer is A.

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Detailed Solution

Given number is 7.478478...
Rational numbers:
The numbers which can be expressed in the form of

p q

, where p, q integers, and q ≠ 0, are known as rational numbers.
On dividing p by q, if the remainder becomes zero then the decimal expansion is terminating and if the remainder never becomes zero and Set of digits repeats periodically then the decimal expansion is non terminating repeating. It is also known as non terminating recurring decimal expansion.
7.478478: Rewrite the repeating numbers in a bar form:
7.478478….. =

7 . 478 ¯

Applying decimal expansion of real numbers:
478 is repeating continuously, so it has non terminating repeating (recurring ) decimal expansion.
Hence, 7.478478….. is a rational number.
Therefore, the correct option is 1.

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