Question
Without actual division, show that the following rational numbers is a non-terminating repeating decimal:$\frac{11}{\big(2^3\times3\big)}$

Answer

$\frac{11}{\big(2^3\times3\big)}$We know either $2$ or $3$ is not a factor of $11$, so it is in its simplest form.
Moreover, $(2^3 \times 3) \neq (2^m \times 5^n)$
Hence, the given rational is non-terminating repeating decimal.

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