Question
Without actual division, show that the following rational numbers is a non-terminating repeating decimal:
$\frac{129}{\big(2^2\times5^7\times7^5\big)}$
$\frac{129}{\big(2^2\times5^7\times7^5\big)}$
✓
Answer
$\frac{129}{\big(2^2\times5^7\times7^5\big)}$
We know $2, 5$ or $7$ is not a factor of $129$, so it is in its simplest form.
Moreover, $\left(2^2 \times 5^7 \times 7^5\right) \neq\left(2^m \times 5^n\right)$
Hence, the given rational is non-terminating repeating decimal.
We know $2, 5$ or $7$ is not a factor of $129$, so it is in its simplest form.
Moreover, $\left(2^2 \times 5^7 \times 7^5\right) \neq\left(2^m \times 5^n\right)$
Hence, the given rational is non-terminating repeating decimal.
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