to add 1/3 in decimal together 3 times, you'd have to add the infinite number of 3's at the end.
the only way for it to be exactly 1/3 is for it to have an infinite number of 3's
people can't add an infinite number of digits together.
to add 1/3 in decimal together 3 times, you'd have to add the infinite number of 3's together. if you somehow could add the infinite number of 3's together, then it would be exactly 1.
but if you end it somewhere, then of course it will be less than one.
however by ending it somewhere, it wouldn't be exactly 1/3, since the exact number has an infinite amount of 3's at the end.
therefore by ending it somewhere, you wouldn't get the right answer
infinite decimal places are the reason people came up with fractions.
fractions are used to define some of the numbers which would be irrational in decimal form.
there are also other irrational numbers, which are defined by surds (using square, cube, quad etc. roots of numbers)
but some irrational numers cannot be defined in the base-10 number system that we use. therefore we cannot find those numbers exactly. we just round those numbers off, and call it an approximation