00:01
So for this question, we're trying to figure out how long it's going to take you to count the number of particles in a mole.
00:09
So first, we're asked to assume that it takes one second to count one number.
00:20
So we're going to write this as a rate.
00:23
So we'll write this as a rate.
00:24
We'll say that to count one number, it takes one second.
00:32
So this will be our rate.
00:34
You could also write it as it takes one number.
00:39
We can count one number per second.
00:41
So one number per second.
00:43
And that's going to be our rate.
00:47
For the second question, we're asked to convert that into numbers per year.
00:54
So we start out with our rate of one number per one second.
00:59
And we have to convert seconds into years.
01:03
Years.
01:04
So we have to do several conversions.
01:06
So first, let's convert seconds into minutes.
01:09
So we have 60 seconds for every one minute.
01:16
Seconds on bottom, cancel out with seconds on top.
01:18
Now we have to convert minutes into hours, which we have 60 minutes for every one hour.
01:26
Minutes on bottom, cancels out with minutes on top.
01:28
Now we convert hours into day.
01:30
So we have 24 hours for every one day hours on bottom canceled out hours on top now we turn days into years so we have 365 days for every one year days canceled days and so our units that we're going to be left with is numbers on top and years on bottom which will be numbers per year then in your calculator types one times 60 times 60 times 24 times 365 and you should get 3 .15 times 10 to the seventh numbers per year.
02:20
So that's how many numbers per year you'll be able to count.
02:24
You can count 3 .15 times 10 to the seventh numbers per year.
02:29
Now for the next question, how many numbers could you count in a lifetime? so we're going to multiply the numbers per year.
02:39
So we'll take that from the previous question.
02:42
So we have 3 .15 times 10 to the seventh numbers for every one year.
02:53
And then we're going to convert years into lifetime.
02:56
So we're going to say we have 70 years per one lifetime.
03:05
Year on bottom, cancel out with years on top.
03:07
So our units that we're going to be left with is numbers per lifetime.
03:10
So take 3 .15 times 10 to the seventh times 70...