Question

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. Also, find the decimal expressions of the rational numbers.

64

255​

Answer 1

Step-by-step explanation:

64/255

Factors

64 : 2×2×2×2×2×2=2^6

255 : 3×5×17

Now,64/255=2^6/3×5×17

It has non terminating decimal expansion because it is not in the form 2^m5^n

The decimal expansion of the rational number is 0.25490....