Hello, Sophia,
We need to use time conversion factors to change cigarettes/sec to cigarettes/year.
I've loosely arranged them in four separate columns. You should be able to recognize the standard definitions of time in seconds, minutes, hours, etc. Each column is a conversion factor. The top is equal to the bottom (e.g., 1 min = 60 secs). This means we wind up with an expression equivalent to "1" since all numerators are equivalent to their denominators. There is a number associated with it, but that's a number required to change the units, not the actual value.
Cancel the units where you can. You'll see that you are left with just sec/year as the unit. That's what we want so that we can change the original cigarette rate of cigs/sec to cigs/year.
I get 3.15E07 secs/year. Multiply that times 2.0E04 cigarettes/sec, and you wind up with 6.31E11 cigarettes/year.
That's a bundle, you might say. But how many is that, really? Our minds have a hard time interpreting these types of numbers, so let's try another conversion factor analysis:
An average cigarette length is 70 mm. That means a year's worth of cigarettes would stretch 4.42E13 mm, if placed end-to-end. Zounds! But that doesn't really tell us anything, either. Let's change that number into other units.
There are 304.8 mm in a foot, and
5280 feet in a mile
So we get 1.61E6 mm/mile
We can invert that to make it mile/mm = 6.21E-07 mile/mm
Then multiply that time the length of all the cigarettes:
6.21E-07 mile/mm x 4.42E13 mm =2.74E07 miles.
Wow, that's a long walk. The distance from the Earth to the moon is 238,900 mi (2.39E5).
Divide the cigarette length by the distance to the moon:
2.74E07miles/2.39E5miles to the moon = 1.12E02 !!
Those cigarettes will reach from the Earth to the moon 112 times. That's way conversion factors are helpful. We can express the same information in different formats - ones that are more helpful in our understanding.
I hope this helps,
Bob
Robert S.
09/25/20