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If the rational number $a b$ has a terminating decimal expansion, then b can be expressed in the form ____.

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Detailed Solution

If the rational number

a b

has a terminating decimal expansion, then b can be expressed in the form

(2 x × 5 y)

. For any rational number ‘n’ represented as

p q

, where q is non-zero, if the denominator, i.e., q has its prime factors of the form

(2 x × 5 y)

where x and y are positive integers, then that rational number is said to be have a terminating decimal expansion.
So, we can say that the denominator b can be expressed as a product of its prime factors in the general form

(2 x × 5 y)

,where x and y both are positive integers.
Therefore, the blank in the statement will be filled by

(2 x × 5 y)

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