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Without Actual Division Show that Each of the Following Rational Numbers is a Non-terminating Repeating Decimal. (I) `32/147` - Mathematics

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

(i) `32/147`

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Solution

`32/147 = 32/(3 ×7^2)`
We know either 3 or 7 is not a factor of 32, so it is in its simplest form.
Moreover, (3 × 72) ≠ (2m × 5n
Hence, the given rational is non-terminating repeating decimal.

Concept: Euclid’s Division Lemma
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