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# Without Actual Division Show that Each of the Following Rational Numbers is a Non-terminating Repeating Decimal. (I) 9/35 - Mathematics

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

(i) 9/35

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#### Solution

9/35 = 9/(5 ×7)

We know either 5 or 7 is not a factor of 9, so it is in its simplest form.
Moreover, (5 × 7) ≠ (2m × 5n
Hence, the given rational is non-terminating repeating decimal.

Concept: Euclid’s Division Lemma
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