Expert: Josh - 11/15/2007

Question
Hello:

Consider the percentage 25 1/3%. This equals (25 1/3)/100 and expressed as a decimal equals 0.25 1/3.

Is there any way to prove that 1/3 shares the 1/100 place along with the 5 from the decimal 0.25 1/3 and not in the 1/1000 place?

I thank you for your reply.


Answer
Kenneth,

I am not sure that we need a proof, but this is how I see it. Consider 25 1/3. What is the fractional part "1/3" relative to? It is relative to the unit occupied by the integer part which precedes it. What does 25 mean? In this example, 25 is 25 lots of "ones". i.e., 25 = 25 x 1. The unit value of the digit 5 is "one". So, the following fraction "1/3" is also relative to "one". i.e., 1/3 has a value of 1/3 x 1.

The same applies in the case of 0.25 1/3. Mixing decimal and fraction is not something that I like doing, but I guess it is used in commerce as some would argue that this is more intuitive. Anyway, here the "25" is relative to multiples of 0.01. This is the unit value of the integer part which precedes the fraction. So, the fraction 1/3 is also relative to 0.01. Hence, the part "1/3" in this context has a true value of 1/3 x 0.01. This represents one third of a percentage point.