I was wondering, is it possible to multiply 0.333...*0.666... and get the correct result of 0.222... without first turning the repeating decimals into fractions.
I have played with a couple of ideas
Is it possible to multiply the 2 summations together?
I have also looked at 0.333...*0.666... = 3(6/10+6/10^2+6/10^3+....)
But I am wodering where to go from here.
Any ideas would be appreciated.
My conclusion is that turning them into fractions then multipying is the simplist way. I do want to see other methods, practical or not.
Thank you for your time