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Without Actual Division Show that Each of the Following Rational Numbers is a Non-terminating Repeating Decimal. (I) `29/343` . - Mathematics

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

(i) `29/343` 

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Solution

`29/343 = 29/(7^3)`
We know 7 is not a factor of 29, so it is in its simplest form.
Moreover, 73 ≠ (2m × 5n)
Hence, the given rational is non- terminating repeating decimal.

Concept: Euclid’s Division Lemma
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