Question

Without actual performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminationg repeating decimal expansion :
(i) `(12)/(125)` (ii) `(7)/(1600)` (iii) `(11)/(3125)`

Answer 1

(i) `(12)/(125) = (12)/(5 xx 5 xx 5) = (12)/(5^(3)) = (12)/(2^(0) xx 5^(3))`
Now, denominator is in the form of `2^(m) xx 5^(n)`.
`therefore` `(12)/(125)` is a terminating decimal.
(ii) `(7)/(1600) = (7)/(2 xx 2 xx 2 xx 2 xx 2 xx 2 xx 5 xx 5) = (7)/(2^(6) xx 5^(5))`
(iii) `(11)/(3125) = (11)/(5 xx 5 xx 5 xx 5 xx 5) = (11)/(2^(0) xx 5^(5))`
Now, denominator is in the form of `2^(m) xx 5^(n)`.
`therefore (11)/(3125)` is a terminating decimal.