What type of number can be written as a fraction a over b, where a and b are integers and b is not equal to zero?

This is the definition of rational number.

These include: Integers, Terminating Decimals, Repeating Decimals, or Proper, Improper, and Mixed Fractions where each part is an integer.  

Step-by-step explanation:

This is the definition of rational number.

Here are some examples of rational number:

-3  (negative integers are included because they can be rewritten; here -3=-3/1)

5 (positive integers are included because they can be rewritten; here 5=5/1)

0 (neutral integers are included also because 0/4 or 0/1 are still 0)

5/3 (impropert fractions where top and bottom are integers; this is already written in the form required)

1   2/3  (mixed fractions because they can rewritten as improper fractions with top and bottom as integers; example here this 5/3)

2/5  (proper fractions where top and bottom are integers; this is already written in the form required)

.55555555555...= (repeating decimals; example this one can be written as 5/9)

.23 (terminating decimals; example this can be written as 23/100 )

1/800 is the right answer