Question

Q1. Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or non-terminating repeating decimal expansion:




(i)
$\frac{13}{3125}$
​

Answer 1

$\huge\underline\mathsf\purple{ᴀɴsᴡᴇʀ :- }$

$\underline{\frak{\dag \; lcm \: of \; 3125: - }} \\ \\ \begin{gathered}\begin{gathered}\Large{ \begin{array}{c|c|c} \tt 5 & \sf \orange{3125}& \sf \\ \tt5 & \sf \orange{625}& \orange{ }  \\ 5& \sf \orange{125 } & \sf \ \\ 5& \sf \orange{25 } \\ 5& \sf \orange{5 } \\ & \sf \orange{1} \orange{}\end{array}}\end{gathered}\end{gathered}$

$\boxed{ \pink{ \sf ⇨\frac{13}{ {5}^{5} } }} \:$

$\boxed{ \pink{ \sf⇨ It \: is \: terminating}} \:$

ʜᴀᴘᴘʏ ʟᴇᴀʀɴɪɴɢ ...!!! :D

Answer 2

Step-by-step explanation:

Here, the factors of the denominator 10500 are 2²× 3× 5³× 7, which is not in the form 2ⁿ 5^m . Hence, 935/10500 has non terminating repeating decimal expansion.