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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?

Language:
English Language

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.

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.

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