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
Answer:
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
