decimals and fractions

2 = x
3 100
The 100 represents 100/100 parts of 1, so x is a percent.

200 3x
2 = x
3 100
Now you cross multiply 100*2 and x*3. These values will equal each other, so you now need to write an equation.
200= 3x
3 ~~ 3
you divide each side by 3 and get
66.6% repeating, equal to .6 repeating.
_
.6

Normal division.
2 : 3

2 is bigger than 3, so we know it must be a number less than 1 (0,xxxx)

Now append a zero to 2:

[1] 20 : 3 = (18 + 2) : 3 = 18/3 + 2/3 = 6 + 2/3

So far we have 0,6xxx

But as you can see, wie have the same division (2/3) again. Now repeat [1]...