Question

Without actually performing the long division , state whether the rational number 6 divede 80 will have terminating or non terminating decimal expansion

Answer 1

Given :-

$\frac{6}{80}$


We can factories

80 :- 2 × 2 × 2 × 2 × 5


Which can be written as

80 :- 2⁴ × 5


And as we know that if the prime factorisation of denominator is in the form of 2 ^m × 5^n where m and n are non negative integer then fraction has a decimal expansion which terminate .


Hence it is terminating.

and it will terminate after 4 points .