Without actual division , show that each of the following rational numbers is non -terminating repeating decimal :

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HCF and LCM

Recurring Decimal Number

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Question

Without actual division , show that each of the following rational numbers is non -terminating repeating decimal : $\frac{9}{35}$

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$\frac{9}{35} = \frac{9}{5 \times 7}$
5 or 7 is not factor of 9 so fraction is in its simplest form.
and,(5 × 7) ≠ (2^m × 5ⁿ) in denominator
hence given fraction is non -terminating repeating decimal.