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CAHSEE Math 1.2 Number Sense 382 Views


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Description:

CAHSEE Math Number Sense: Drill Set 1, Problem 2. The decimal 0.000035 can be written in scientific notation as...what?

Language:
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Transcript

00:03

Here's a boring, unshmoopy question you'll find on an exam somewhere in life...

00:08

The decimal 0.000035 can be written in scientific notation as... what?

00:15

Here are the potential answers...

00:21

OK, so what's this question really asking?

00:23

Well, it's all about how you simplify writing a realllllly small number.

00:28

Just as when we raise 10 to a positive number it gets big fast...

00:32

...the opposite happens when we raise it to a NEGATIVE number.

00:35

We know that the standard form of writing in scientific notation is a single digit integer

00:41

followed by a decimal and then a bunch of numbers...

00:43

...so then the whole thing is raised to some power, either positive or negative,

00:47

depending on if we want to move the decimal to the left or right.

00:50

And technically the power is 0 if we just want the integer.

00:54

So the first part of the problem needs us to get to a 3.5.

00:58

Let's figure out how to get there before we do anything else.

01:02

Well, we start with 0.000035.

01:06

The decimal has to get from here. To here. No tolls.

01:10

So we move it to the RIGHT -- 1 2 3 4 and 5 places.

01:15

We moved it 5 to the right so we have to now "account" for that move by putting up

01:19

the power which is -- yep -- negative 5.

01:22

If we ever forget whether the power should be positive or negative depending on if whether

01:27

move it left or right... ...we can just remember that if the power

01:30

is positive, the actual number is going to be greater than 10...

01:34

...and if the power is negative, the actual number will be less than 10.

01:38

And we write it like this: 3.5 × 10 to the -5

01:42

The answer is A.

01:43

Note how close D was those... those test-making

01:46

buggers are always trying to trip us up...

01:48

so let's not forget the negative sign.

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