Question
Without actual division, show that the following rational numbers is a non-terminating repeating decimal:
$\frac{32}{147}$
$\frac{32}{147}$
✓
Answer
$\frac{32}{147}=\frac{32}{3\times7^2}$
We know either $3$ or $7$ is not a factor of $32$, so it is in its simplest form.
Moreover, $\left(3 \times 7^2\right) \neq\left(2^m \times 5^n\right)$
Hence, the given rational is non-terminating repeating decimal.
We know either $3$ or $7$ is not a factor of $32$, so it is in its simplest form.
Moreover, $\left(3 \times 7^2\right) \neq\left(2^m \times 5^n\right)$
Hence, the given rational is non-terminating repeating decimal.
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