A closed container has 2.04 ⋅ 1023 atoms of a gas. Each atom of the gas weighs 1.67 ⋅ 10−24 grams. Which of the following shows and explains the approximate total mass, in grams, of all the atoms of the gas in the container?

0.34 grams, because (2.04 ⋅ 1.67) ⋅ (1023 ⋅ 10−24) = 3.4068 ⋅ 10−1
0.37 grams, because (2.04 + 1.67) ⋅ (1023 ⋅ 10−24) = 3.71 ⋅ 10−1
3.41 grams, because (2.04 ⋅ 1.67) ⋅ (1023 ⋅ 10−24) = 3.4068
3.71 grams, because (2.04 + 1.67) ⋅ (1023 ⋅ 10−24) = 3.71

Question

A closed container has 2.04 ⋅ 1023 atoms of a gas. Each atom of the gas weighs 1.67 ⋅ 10−24 grams. Which of the following shows and explains the approximate total mass, in grams, of all the atoms of the gas in the container?

 0.34 grams, because (2.04 ⋅ 1.67) ⋅ (1023 ⋅ 10−24) = 3.4068 ⋅ 10−1
 0.37 grams, because (2.04 + 1.67) ⋅ (1023 ⋅ 10−24) = 3.71 ⋅ 10−1
 3.41 grams, because (2.04 ⋅ 1.67) ⋅ (1023 ⋅ 10−24) = 3.4068
 3.71 grams, because (2.04 + 1.67) ⋅ (1023 ⋅ 10−24) = 3.71

cqluv · Answer

hello

anonymous · Answer

Did you mean to write
$$10^{23}$$$$10^{-24}$$
It can also be written as 10^23 and 10^-24

Since in the problem it is written correctly (2.04 * 10^23) and (1.67 * 10^-24) you can rule out the 2 solutions that have the + sign in it.  Which leaves us with:
(2.04*1.67) * (10^23*10^-24)

Without using a calculator we can round and rewrite the problem as (2)(2)(10^23)(10^-24).  Which is:
$$4*10^{23-24} = 4*10^{-1} = 0.4$$

If you put in the calculator (2.04*1.67) * (10^23*10^-24) you'll get the exact value.