Without Actual Division Show that Each of the Following Rational Numbers is a Non-terminating Repeating Decimal. (I)64/455 - Mathematics

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

(i)64/455

Solution

64/455 = 64 /(5 ×7 ×13)

We know 5, 7 or 13 is not a factor of 64, so it is in its simplest form.
Moreover, (5 × 7 × 13) ≠ (2m × 5n
Hence, the given rational is non-terminating repeating decimal.

Concept: Euclid’s Division Lemma
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