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need a tip for calculation

Expert replies
by HPengineer » Sun Dec 26, 2010 10:52 pm
a problem states that .0063 percent of the population = 10 people

what is the total population?

can i say that .0063 = 63/10,000?? then solve by (63/10,000)X = 10 x being the total population?
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Source: — Problem Solving |

by Anurag@Gurome » Sun Dec 26, 2010 11:07 pm
HPengineer wrote:a problem states that .0063 percent of the population = 10 people

what is the total population?

can i say that .0063 = 63/10,000?? then solve by (63/10,000)X = 10 x being the total population?
Yes, you can say that 0.0063 = 63/10,000
But the part highlighted in red is not correct.

0.0063% of the total population = (0.0063/100)*(Total population)
If x is the total population, then
  • (0.0063/100)x = 10 => (63/1,000,000)x = 10
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by HPengineer » Sun Dec 26, 2010 11:11 pm
so if they give me a percent just write it over 100 no matter how small it may be??

.00781 % of something is simply .00781/100 *(something)
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by Anurag@Gurome » Sun Dec 26, 2010 11:13 pm
HPengineer wrote:so if they give me a percent just write it over 100 no matter how small it may be??

.00781 % of something is simply .00781/100 *(something)
Absolutely! :)
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by fskilnik@GMATH » Tue Dec 28, 2010 5:53 am
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.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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