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Question
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.
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