Without actual division find whether 18/30 will have a terminating decimal expansion or a non-terminating repeating decimal

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Solution

Dear Student,

$We know that, a rational number has a terminating decimal expansion if the prime factorisation of the denominator is of the form of 2^{m} 5^{n}, where m and n are non negative real numbers . Now, given number = \frac{18}{30} = \frac{3}{5} = \frac{3}{2^{0} \times 5^{1}} Since, the denominator is of the form of 2^{m} 5^{n}, where m and n are non negative real numbers, hence the given number has terminating decimal expansion .$
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