Question
Without actual division, show that the following rational numbers is a non-terminating repeating decimal:
$\frac{77}{210}$
$\frac{77}{210}$
✓
Answer
$\frac{77}{210}=\frac{77\div\text{7}}{210\div7}$
$=\frac{11}{30}=\frac{11}{2\times3\times5}$
We know $2, 3$ or $5$ is not a factor of $11$, so $\frac{11}{30}$ is in its simplest form.
Moreover, $(2 × 3 × 5) ≠ \left(2^m \times 5^n\right)$
Hence, the given rational is non-terminating repeating decimal.
$=\frac{11}{30}=\frac{11}{2\times3\times5}$
We know $2, 3$ or $5$ is not a factor of $11$, so $\frac{11}{30}$ is in its simplest form.
Moreover, $(2 × 3 × 5) ≠ \left(2^m \times 5^n\right)$
Hence, the given rational is non-terminating repeating decimal.
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