A percent is actually a fraction already. (If you break up the words to have "per cent," this might seem more intuitive. "Cent" is from Latin centum, and is the same root in words like century. Here, it's like per hundred.)
You probably know intuitively that 100% is one whole, for example. But it's also the same as saying [tex] \frac{100}{100} [/tex]. Likewise, 67%, for instance, is actually [tex] \frac{67}{100} [/tex].
In this case, you can write [tex] \dfrac{0.6}{100}[/tex]. But you may realize that you shouldn't have a decimal in a fraction. For every number after the decimal, you multiply the whole thing by a corresponding power of ten. Here, you write [tex] \dfrac{0.6}{100} * \dfrac{10}{10} = \dfrac{6}{1,000} [/tex]. Since 10/10 is equal to 1, we aren't changing anything (Identity Property). If you had 0.06/100, you would multiply by 100/100, and so on...
So, now we have [tex] \dfrac{6}{1000} [/tex]. Our next step is to simplify. The greatest common factor of these two numbers is 2, we rewrite as [tex] \dfrac{3}{500} [/tex] to put it into simplest form. And that's all there is to it.
