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word problem

bergausstein

Active member
Jul 30, 2013
191
Atmospheric concentrations are usually measured
in parts per billion, by volume (ppbv). So, a concentration of carbon dioxide equal to 13 ppbv means that, for every billion volume units (say,milliliters) of the atmosphere, there are 13 units of carbon dioxide.
Convert an atmospheric concentration of carbon
dioxide of 13 ppbv to a percent (that is, what per-cent of this atmosphere would be carbon dioxide?)

my solution

$\frac{13}{10^9}=1.3\times 10^{-8}$

is this correct. if not please help me arrive at the correct answer. thanks!
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
We know that \(\displaystyle \frac{1}{2}=50\%\) or:

\(\displaystyle \frac{1}{2}=\left(\frac{1}{2}\cdot100 \right)\%=50\%\)

We see that when converting a fraction to a percentage, we must treat the percent sign as division by 100, because per cent literally means "for each 100." So if we attach a percent sign, we must multiply the fraction by 100 so that we are in effect multiplying by:

\(\displaystyle 1=\frac{100}{100}=100\cdot\frac{1}{100}=100\%\)

Hence:

\(\displaystyle \frac{a}{b}=\frac{100a}{b}\%\)

Can you proceed?
 

bergausstein

Active member
Jul 30, 2013
191
I still don't get it.

it's because of parts per billion thing. i'm confused. how am I suppose to convert 13ppbv to a percent? please bear please bear with me.
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
What you need to do is:

\(\displaystyle \frac{13}{10^9}=\frac{13\cdot10^2}{10^9}\%\)

Now simplify. :D