Final answer:
13 1/3 percent as a fraction in simplest form is 2/15. To achieve this, you combine the fraction for 13 percent (13/100) with the fraction for 1/3 percent (1/300) and simplify the resulting fraction (40/300) by dividing by the greatest common divisor.
Step-by-step explanation:
To express 13 1/3 percent as a fraction in simplest form, begin by converting the percent to a fraction. The given percent is the same as 13.33...%, where the '...' indicates that the '3' is repeating. A fraction with a repeating number can be written using a specific technique, but let's first simplify the process by considering 13 1/3 percent as 13 + 1/3 percent. Thirteen percent as a fraction is 13/100. To convert the 1/3 percent, remember that 1 percent is 1/100, so 1/3 percent would be (1/3) / 100 or 1/(3×100). This equals 1/300.
Now, combine the two fractions (13/100 and 1/300) having a common denominator, which is 300. Multiply the fraction 13/100 by 3/3 to get 39/300. Then add this to 1/300, resulting in 40/300.
The last step is to simplify the fraction 40/300, by dividing both the numerator and the denominator by their greatest common divisor which is 20, yielding 2/15.