Hi reto,

This question is complex-looking (since it includes Scientific Notation), but it's really just a ratio question.

We're given the rate, per minute, that gas molecules are reduced: (6.5)(10^24) molecules/minute

We're asked, in MINUTES, how long it would take to reduce the number of molecules by (30)(10^21).

To make the comparison more "apparent", I'm going to rewrite the second number...

(30)(10^21) = (3)(10^22).

Comparing these two values...

(3)(10^22) and (6.5)(10^24)

...it should be clear that (6.5)(10^24) is LARGER. Since it takes 1 minute to clear that many molecules, it should take LESS than 1 minute to clear (3)(10^22) molecules. From here, we just need to create a ratio....

(3)(10^22) / (6.5)(10^24)

(10^22)/(10^24) = 1/(10^2)

3/6.5 is about 1/2

This leaves us with....

about 1 / (2)(10^2) = about 1/200 minutes

1/200 = .005 minutes

Final Answer:

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Rich

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