Examine whether the following number is rational or irrational:
$5.040040004 . . .$

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Solution

Examining whether the given number is rational or irrational
The decimal expansion of an irrational number is non-terminating non-recurring. So, a number whose decimal expansion is non-terminating non-recurring is irrational.
The number $5.040040004 . . .$ is non-terminating and non-recurring.
Hence, $5.040040004 . . .$ is an irrational number.

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