Question

The decimal expansion of 256/125 is non terminating repeating

Answer 1

Answer:

No, 256/125 will terminate after 3 decimal places

Answer 2

$Given \: rational \: number \: \frac{256}{125}$

$= \frac{256}{5^{3}}$

$Denominator \: is \: of \: the\:form \: 2^{n} 5^{m}$

$so, it \: is \: a \: terminating \: decimal .$

$= \frac{256\times 2^{3}}{5^{3} \times 2^{3}}$

$= \frac{256\times 8}{(5\times 2)^{3}}$

$= \frac{ 2048}{10^{3}}$

$= \frac{2048}{1000}$

$= 2.048 \: \blue{ ( Terminating \: decimal )}$

Therefore.,

$\red{\frac{256}{125} }\green { = 2.048}$

$\blue{ ( Terminating \: decimal )}$

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