Question

Without actually performing the long division the terminating decimal expansion of 2/25 is in the form of 8/2m5n, then (m+n)=​

Answer 1

$m = 2 \: \: \: and\: \: \: n = 2$

Step-by-step explanation:

$Given, \: \: \: \frac{2}{25} \\ A/Q, \: \: \: \: \: \: \: \: \: \: \frac{2}{25} = \frac{8}{ {2}^{m} {5}^{n} } \\ Now, \: \: \: \: {2}^{m} {5}^{n} = 8 \times \frac{25}{2} \\ {2}^{m} {5}^{n} = 4 \times 25 \\ {2}^{m} {5}^{n} = {2}^{2} \times {5}^{2} \\ By \: \: comparison \\ \: \: \: \: \: \: \: \: \: \: \: \: \: {2}^{m} = {2}^{2} \: \: \: and \: \: \: {5}^{n} = {5}^{2} \\so, \: \: m = 2 \: \: \: and\: \: \: n = 2$

Answer 2

Answer:

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