# 1/3 is equal to .333333

My friend thought of this some time ago.........
1/3 is equal to .333333...
2/3 is equal to 2*(1/3) or .66666...
3/3 is equal to 3*(1/3). If 1/3 is equal to .333... then wouldn't 3/3 be equal to .9999...? Also, isn't .9999... not the same as 1?

You should search this. Analogues of this question have come up before.

Hurkyl
Staff Emeritus
Gold Member
Also, isn't .9999... not the same as 1?
Double negatives! I don't think you're asking quite what you meant to ask.

0.999~ is the same number as 1. That the same number can have different symbolic representations shouldn't be surprising... after all, you know that the fractions 1/2 and 3/6 are the same number!

Examples like the one you posted are demonstrations of why mathematicians decided to require that 0.999~ = 1 in the decimal number system: otherwise arithmetic would not work nicely.

HallsofIvy