valence, imagen this
0,3*3=0,9
0,33*3=0,99
0,333*3=0,999
so if 1/3 is finite amount of decimals then you won't get 1 when its multiplied with 3, you just get a long line of 9s. while a infinite amount of nines after each other equals one since
x=0,9999...
10x=9,9999...
9x=9
x=1
and...