How many ballons, each containing 6.02 × 10^23 particles of helium gas, can be filled from a tank that contains 1.204 × 10^25 helium particles?

Question

How many ballons, each containing 6.02 × 10²³ particles of helium gas, can be filled from a tank that contains 1.204 × 10²⁵ helium particles?

Answer 1

We have 1.204 x 10^25 particles to be divided among balloons, each of which holds 6.02 x 10^23 particles. To find number of balloons to be filled, divide:  (1.204 x 10 ^ 25) / (6.02 x 10 ^ 23), which is (12.04 x 10^ 24) / (6.02 x 10 ^ 23), which comes out to be 2 x 10 ^ 1, which is 2 x 10, which is 20 balloons. I converted 1.204 to 12.04 by multiplying by 10, but then must convert 10^25 to 10^24 by dividing by 10. This makes division of the non-exponent numbers come out to be a whole number. Then, dividing the 10^24 by 10^23 just involves subtracting the exponents, thus 24 - 23 = 1, so the exponent in the answer is 1.