# Without Actual Division Show that Each of the Following Rational Numbers is a Non-terminating Repeating Decimal. (I) 129/(2^2× 5^7 × 7^5) - Mathematics

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

(i) 129/(2^2× 5^7 × 7^5)

#### Solution

129/(2^2× 5^7 × 7^5)

We know 2, 5 or 7 is not a factor of 129, so it is in its simplest form.
Moreover, (22× 57× 75) ≠ (2m × 5n)

Hence, the given rational is non-terminatin g repeating decimal.

Concept: Euclid’s Division Lemma
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