Expert: Josh - 8/10/2007

Question
how do i turn 33% and 9% into a fraction and are their any percentages that the denominator remains 100, being that they are unable to be simplified

Answer
Hello Joanne,

A percentage point is equivalent to 1/100. So, we can represent 33% with the fraction 33/100, which is obtained from 33 x (1/100). Similarly, 9% corresponds to 9/100. If you wish, this fraction may be written as in decimal form as 0.09. This can be seen from long division, alternatively, you can evaluate 9 / 100 on a calculator.

Note: If we have 33 and 1/3% (0.3333333... in decimal), this amounts to one third, "1/3".

Regarding your second point, X% can be written as X/100. If we consider 4%, we have 4/100. Dividing both the numerator (top) and denominator (bottom) by 4, we get 1/25.

When the number X in the fraction X/100 is relatively prime with 100 (i.e., the two numbers have no factors in common) the fraction will be irreducible (i.e., it will stay as X/100 and cannot be further simplified).

e.g., If X=7 (say, we have 7%), 7/100 is irreducible. Since 100=2x2x5x5, the fraction is guaranteed to be irreducible if we pick prime numbers as X, other than 2 and 5. Possible values include X=3,7,11,13,19,23,29,31 etc. For instance, 19/100 is irreducible.