Question

State wheter 23/2325 Will have a terminating decimal expansion or a non terminating repeating decimal

Answer 1

2325=5×465
=5×5×93
=5×5×3×31
here the expansion of 2325 contain 31 which indivisible number so the expansion will have non terminating reapiting decimal

Answer 2

23
$\frac{23}{2325} \\ \frac{23}{5 \times 5 \times 3 \times 31 } \\ so \: if \: the \: denominator \: is \: in \: the \: form \: of \: {2}^{n} \times {5}^{m} than \: it \: is \: terminating \: but \: if \: any \: other \: number \: is \: also \: multiplied \: with \: it \: as \: 31 \: and \: 3 \: is \: multiplied \: than \: the \: answer \: is \: non \: terminating \: but \: repeating \\ so \: your \: answer \: is \: non \: terminating \: but \: repeating$