is the answer 0.00544 ?

Determine whether the following number have a terminating decimal expansion or non-terminating repeating decimal expansion: $\frac{17}{3125}$

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Solution

$We know that a rational number has a terminating decimal expansion if the prime factorisation of denominator is of the form of 2^{m} . 5^{n}, where m and n are non negative integers . The given number is \frac{17}{3125} Now, \frac{17}{3125} = \frac{17}{5 \times 5 \times 5 \times 5 \times 5} = \frac{17}{5^{5}} So, the given number has terminating decimal expansion . Now, \frac{17}{3125} = \frac{17}{5^{5}} = \frac{17 \times 2^{5}}{5^{5} \times 2^{5}} = \frac{544}{100000} = 0.00544$

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is the answer 0.00544 ? Determine whether the following number have a terminating decimal expansion or non-terminating repeating decimal expansion: 173125

is the answer 0.00544 ?

Determine whether the following number have a terminating decimal expansion or non-terminating repeating decimal expansion: $\frac{17}{3125}$