ShmoopTube
Where Monty Python meets your 10th grade teacher.
Search Thousands of Shmoop Videos
Basic Operations Videos 58 videos
It's impressive that these expressions are able to stay so rational even when they're having operations performed on them.
Jack and Jill went up the hill to fetch a pail of water. But what happened when they got up there? They’ve been gone an awfully long time…
CAHSEE Math 1.1 Number Sense 743 Views
Share It!
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.
Related Videos
CAHSEE Math: Algebra and Functions Drill 5, Problem 3. Solve the equation.
We don't like knocking people down to size, but we do like simplifying radicals. Join us?
If fleeing criminals always fled the scene of the crime at perfect right angles, it would be much easier to determine their whereabouts. Fortunatel...
Okay, so this probably isn't going to help you master Pokemon Go, but game theory can be applied to all sorts of situations. Even stomping your old...