Hi there,
Let me contribute to this theme...
01. The symbol % may be substituted by 1/100 or by 10^(-2) simply because % means PER CENT, that is, OVER 100.
Have a look at these examples:
(a) 14% of 10^5 is 14*10^(-2)*10^5 = 14*10^3 = 14,000
(b) 14 over 300 = 14 over (3*100) = (14/3) * (1/100) = 14/3 % and to be classy... 14/3 = (12+2)/3 = 4+2/3 therefore 14/300 is equal to (4 and 2/3) %, that is, approx. 4.66%
02. As questioned, it is common to look for "the total" when it is given that (say) 123 is 17% of this "total". For that purpose,
You may write (of course) (17/100)* total = 123 and then total = 123 over 17% (as Anurag explained)
BUT you can also "imagine" the ratio of 123 to 17% (in that order) is "interpreted" like 123 as 100% of the 17% given, therefore we will find "the 100% such that 17% of it is exactly 123" by the ratio suggested...
Explicitly: if you divide 123 by 17% , that is, if you multiply 123 by (100/17), you will get the "total" immediately.
(I know this is a consequence of the first "method", but you can understand the interpretation and use the shortcut without putting the equation first...)
Example: .0063 percent of the population = 10 people
Means the total number of people is 10 / (.0063/100) = 10 over 63*10^(-6) = 10^(7) over 63.
Regards,
Fabio.
