ok so i understand it's impossible to represent .01(decimal) in binary...an example i know of would be just like how 1/30 is impossible to represent in decimal

1/30 <--- always gives u .033333.....it goes on forever and i can even prove this by writing out 1 divided by 30 and i notice i keep getting the same number over and over and i am in an infinite loop. my question is how can i prove that .01 cannot be represented in binary form,without using a repeating decimal division problem? in other words i can i prove this by USING only binary digits to get my point across?

is .01(decimal) even representable in binary?