$151600$ is a ____ decimal.

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Detailed Solution

151600

is a terminating decimal.
We can rewrite the number as follows,

151600 = 15 2 × 2 × 2 × 2 × 2 × 2 × 5 × 5 = 15 26 × 52

For any rational number ‘n’ if the denominator, 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 observe that the denominator is

(26 × 52) = (2 x × 5 y)

, which means that the rational number will terminate.
Therefore, we conclude that

151600

is a terminating decimal.

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