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.333... Is a third. That's just a quirk of base 10. If you go to a different number system you won't run into that particular issue.
The most common other base people know of is binary. Base 2. So in binary the fraction would be 1/11 and then 1/11(binary)=1/3(base 10).
I remember talk back in the day that base 12 is good for most common human problems. Some people were interested in trying to get people to switch to that.
1/3 of 12 is 4.
So 4/12=1/3=3.33333.../10
.333... Is just the cursive way of writing 1/3.
I still don't "grasp" infinity. I'd recon you'd need an infinite mind to grasp infinity.
1/3 of 10 is 3
3 x 3 is 9
Yet
1/3 of 1 is .3
.3 x 3 is 1?
Just does not compute for me.
1/3 of 10 is 3.333...
1/3 of 1 is .333...
It's like when people come to America and are surprised when tax isn't included in sale prices. The .0333... you forgot to add on will get you in trouble with the universes math IRS.