What is two thirds of eight

5 + 0.33333... 

If you don't immediately recognize 0.33333 as 1/3 (a very common fraction you should memorize), you can do the following. 

x = 0.33333... 

Multiply that by 10 to shift everything 1 place to the left: 
10x = 3.33333... 

Now subtract: 
10x - x = 3.33333... - 0.33333... 
9x = 3 
x = 3/9 
x = 1/3 

 
5 1/3 

P.S. Here's a shortcut way to turn a repeating decimal into a fraction. 

1) Take the repeated part and put it over an equivalent number of nines. 

Example: 
0.57575757... = 57/99 

At that point, see if you can reduce the fraction: 
= 19/33 

Another example: 
0.123123123... = 123/999 
= 41/333 

So in your example: 
5.33333... = 5 + 0.33333... 
= 5 + 3/9 
= 5 1/3

That she received $100