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Rational number ( $x = a b, b ≠ 0,$ a and b are integers as well as a and b are co-prime) $37189$ ? Find for how many decimal places do a given rational number terminates?

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It will not terminate

answer is A.

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Detailed Solution

Given a rational number

37189

.
Let us find at what values it terminates
According to the question we have

37189

Check if expression gets converted such that denominator is powers of 10,

37189 = 37 3 × 3 × 3 × 7

Denominator cannot be expressed in powers of 10 that's why it will not terminate.
It will not terminate.
So, the correct option is 4.

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