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Without actual division, show that each ...

Without actual division, show that each of the following rational numbers is a nonterminating repeating decimal.
(i) ` 11/((2^(3) xx3) ` (ii) `73/((2^(2) xx 3^(3) xx5))` (iii) ` 129/((2^(2) xx 5^(3) xx 7^(2)) `
(iv) ` 9/35`
(v) ` 77/210` (vi) `32/147` (vii) ` 29/343` (viii) ` 64/455`

Text Solution

Verified by Experts

(iv) ` 9/35 = 9/( 5xx7) ` (v) ` 77/210 = 11/30 = 11/((2xx 3xx5)) ` (vi) ` 32/147 = 32/ ((3 xx7^(2)))`
(vii) ` 29/343 = 29/7^(3)` (viii) ` 64/455 = 64/((5xx 7 xx 13))`
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