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CAHSEE Math 1.1 Number Sense 743 Views
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Description:
CAHSEE Number Sense: Drill Set 1, Problem 1. How would he write the number in scientific notation?
Transcript
- 00:03
Here's a shmoopy question for you...
- 00:05
Melvin has been in prison for almost 3 years
- 00:07
and, like many of his inmates, he marks his time on the wall of his cell.
- 00:12
However, Melvin likes to mark every second that he's been
- 00:14
incarcerated, rather than just every day.
Full Transcript
- 00:17
He has now been in jail for 86,310,000 seconds...
- 00:22
and he feels like his routine is getting a little stale. Imagine that.
- 00:26
He wants to write the number in scientific notation to... mix things up.
- 00:31
How would he do that? And here are the potential answers...
- 00:36
This question is testing one thing and one thing only...
- 00:38
...did we show up for class the day our teacher taught us what scientific notation is.
- 00:45
No way to brute force it... either we know it or we don't.
- 00:48
If we make a mistake, it's gonna be because we messed up the zeros... where the decimal goes.
- 00:55
So an easy way to check ourselves is to WRITE OUT THE PROBLEM with the decimal. Like this.
- 01:00
Yes. The "point zero" at the end is important in this case.
- 01:05
In scientific notation, the decimal point always ends up behind the first significant digit...
- 01:11
...which in this case, is behind the 8.
- 01:16
Now we just count the places between where
- 01:18
the decimal exists and where it would have to go to sit next to the eight...
- 01:22
...and we just count 1 2 3 4 5 6 and 7 places, moving it to the left.
- 01:29
We moved seven places to the left, to the left... isn't there a Beyonce song like that?
- 01:35
Anyway -- we move 7 places and you'll note that this corresponds beautifully to the way
- 01:40
10 acts when we put it to a... higher power.
- 01:44
That is, 10 squared is to the 2nd power has 2 zeroes; 10 cubed is to the 3rd power
- 01:52
and has 3 zeroes... and so on.
- 01:54
So it'd make sense that 10 to the 7th
- 01:57
would give us a number with 7 integers before the decimal.
- 02:00
When we are playing with this big honkin' multiplier,
- 02:03
the numbers AFTER the decimal actually matter...
- 02:05
...in real life, it'd be easy to just toss out everything after the decimal when the
- 02:09
scale says you weigh 272.342981 pounds. Two seventy-two is big enough.
- 02:16
But here, those numbers matter.
- 02:18
With choice B, for example, we'd be off a bit.
- 02:21
8.63 x 10 to the 7th would give us only 86,300,000 seconds...
- 02:27
and Melvin already carved that number into the wall ages ago.
- 02:32
Well, okay... ten seconds ago, but still... it isn't exact.
- 02:35
So the answer is C... 8.631 × 10 to the 7th.
Up Next
CAHSEE Math: Algebra and Functions Drill 5, Problem 3. Solve the equation.
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