Calculating Carbon Ratio in Living Systems to Total Carbon on Earth

[bjoyful]

Homework Statement

The total mass of carbon in living systems is estimated to be 7.7x10^17 g. Given that the total mass of carbon on Earth is estimated to be 7.7x10^22 g, what is the ratio of carbon atoms in living systems to the total carbon atoms on Earth? Report your answer in percent and in ppm. Do not forget to show your calculation work.

Homework Equations

The Attempt at a Solution

1 * (e^(-5)) = 0.006737947 or 22/17 would give me the percent of 77. I have been going round and round with this question for the last few weeks and now it is due in a couple of days! Also, I want to double check - is total mass of carbon the same as carbon atoms?

 

[mit]

carbon are carbon atoms and if you know that 7.7x10^22 gr 100% is than you can calculate how mutch % 7.7x10^17 gr is. Why do you use e^-5?

 

[bjoyful]

I used e^-5 because that is what the graphing calculator gave as an answer. I am sure about those numbers, but how do I find a ratio or % mathmatically when exponents are used?

 

[mgb_phys]

The 10^-5 is the answer because 7.7x10^17 / 7.7x10^22 is 10^-5 or 0.00001

To do multiplication/division of numbers with exponents just add/subtract the exponents, that's why we use them - it makes these sort of calculations very easy!
ps. Don't write it as e^-5, the lower case 'e' means something very different in maths, write either x10^-5 or E-5.

 

[bjoyful]

Thanks for warning me about the "e"! Why is it a negative 5? Also, if it is 0.00001, then is that considered a %. How do I write it...1/10000%. How do I convert this to ppm? I am trying to understand greek here! Thanks for your help.

 

[mgb_phys]

10^5 is 10 multiplied by itself 5 times = 10*10*10*10*10 = 100000
10^-5 is 10 divided by itself 5 times = 1 / 10*10*10*10*10 = 1/100000 = 0.00001

This is one part in 100,000 so 0.1 parts in 1,000,000.
A percentage is just the fraction multiplied by 100, so 0.5 = 50%, 0.00001 = 0.001%

 

[mit]

e is a Neperiaans logaritmic function so it looks strange to me that it was used. For me 0.001% was the correct answer. If you are not sure about ppm it is part per million

 

[bjoyful]

So for this problem, my answer for ppm would be written 0.1ppm. How would I show my work for that? Thanks

 

[bjoyful]

thanks mit, i couldn't remember what ppm was short for...