Question

without actually performing the long division state whether the following rational numbers will have terminating decimal expansion or non terminating repeating decimal expansion.1)315/16,2)427/625,3)619/325

Answer 1

this answer would help you I think
all the best for your board exams

Answer 2

Answer:

1) & 2) are terminating decimals.

3) is non-terminating and repeating decimal

Step-by-step explanation:

$1) \frac{315}{16}=\frac{315}{2^{4}}$

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

Therefore,

$\frac{315}{16} \: is \\\: terminating\: decimal$

$2) \frac{427}{625}=\frac{427}{5^{4}}$

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

Therefore,

$\frac{427}{625} \: is\\ \: terminating\: decimal$

$3) \frac{619}{325}=\frac{619}{5^{2}\times 13}$

$The \: denominator \: is\\ \:not\: of \: the \: form \: 2^{n}5^{m}$

Therefore,

$\frac{315}{16} \: is \\\: non-terminating\: Repeating \:decimal$

•••♪