Final answer:
To find the number of moles of carbon remaining after burning 33% of the 1 billion carbon atoms, we divide the number of burned atoms by Avogadro's number.
Step-by-step explanation:
To find the number of moles of carbon remaining after burning 33% of the 1 billion carbon atoms, we first need to calculate the total number of carbon atoms burned. 33% of 1 billion is 330 million, or 3.3 x 10^8 atoms. To find the number of moles, we divide the number of atoms by Avogadro's number (6.022 x 10^23 atoms/mol). Therefore, the number of moles of carbon remaining is 3.3 x 10^8 atoms divided by 6.022 x 10^23 atoms/mol, which equals 5.48 x 10^-16 moles of carbon.