Question

Show that :
(i) `(3)/(250)` (ii) `(11)/(50)`
are terminating decimals. Express each of them in decimal form without actual division (long division).

Answer 1

(i) `(3)/(250) = (3)/(2 xx 5 xx 5 xx 5) = (3)/(2^(1) xx 5^(3))`
Now, the denominator is in the form of `2^(m) xx 5^(n)`.
`therefore (3)/(250)` is a terminating decimal. Hence proved.
Again, `(3)/(250) = (3)/(2^(1) xx 5^(3)) = (3 xx 2^(2))/(2^(3) xx 5^(3)) = (12)/(10^(3)) = 0.012`
(ii) `(11)/(50) = (11)/(2 xx 5 xx 5) = (11)/(2^(1) xx 5^(2))`
Now, the denominator is in the form of `2^(m) xx 5^(n)`.
`therefore (11)/(50)` is a terminating decimal.
Again, `(11)/(50) = (11)/(2^(1) xx 5^(2)) = (11 xx 2)/(2^(2) xx 5^(2)) = (22)/(10^(2)) = 0.22`