Without actually performing the long division, state whether the ratio

1.	Without actually performing the long division, state whether the rational number13/3125 will have a terminating or non-terminating decimal expansion.1.
Answer» 3125 = 55555 = 5⁵13/3125= 13/5⁵= (132⁵)/(5⁵2⁵) {Multiplying the numerator as well as the denominator with 2⁵}= (13*32)/(10⁵)= 416/10⁵= 0.00416 It is a terminating decimal. Like my answer if you find it useful!

Without actually performing the long division, state whether the rational number13/3125 will have a terminating or non-terminating decimal expansion.1.

Answer»

3125 = 5*5*5*5*5 = 5⁵13/3125= 13/5⁵= (13*2⁵)/(5⁵*2⁵) {Multiplying the numerator as well as the denominator with 2⁵}= (13*32)/(10⁵)= 416/10⁵= 0.00416

It is a terminating decimal.

Like my answer if you find it useful!