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Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion:(i) ` (13)/(3125) ` (ii) ` (17)/8 ` (iii) ` (64)/(455) ` (iv) ` (15)/1600 ` (v) ` (29)/(343) `
(vi) ` (23)/(2^35^2) ` (vii) ` (129)/(2^25^77^5) ` (viii) ` (6)/(15) ` (ix) ` (35)/(50) ` (x) ` (77)/(210) `

Text Solution

Verified by Experts

Terminating and non terminating decimal can be represented in the factors of `2 and 5`
If denominator has only factor `2 and 5`, it has terminating expansion.
If factors are other than `2 and 5`, then it is non terminating expansion.
(i) `13/3125`
Factorizing the denominator,
`3125 = 5xx5xx5xx5xx5 = 5^5`
Since, only `5` is the factor, it has terminating decimal expansion.
(ii) `17/8`
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