**Scientific Notation Review**

To convert we need to...

Rule #2

**To convert from Standard Notation to Scientific Notation**

**Rule # 1**

To go from Scientific Notation back to Standard Notation, just go in reverse.

**Why use this crap anyway?**

**Well,here are some reasons:**

**Q1)**

**How far away is the Sun?**

**In meters!**

**A1)**

I know it's long ... stay with me.

-the Sun is 92 million miles away...

and there are about 1,600 meters in a mile

So...

OK, time for a little vocab...

Standard Notation:

so this is like the regular number you use every day

12.5

or

12,960,000

Scientific Notation:

This is what we use for

very

large or

very

small numbers

6.5 X 10

7

or

2.35 X 10

-13

For those last two we would say... out loud.

6.5 X 10

7

We would say,

"Six point five times ten to the seventh"

**AND**

2.35 X 10

-13

We say...

"Two point three five times ten to the negative thirteen"

**92,000,000**

**X**

**1,600**

147,200,000,000

meters!

It would be a pain to write that a lot of times!

**Q2)**

**What is Avogadro's number?**

Avogadro's number is how many atoms of something there are in a mole.

... don't worry, more on that in chemistry.

**It is...**

602,214,150,000,000,000,000,000

That is a big number!

Much easier to write...

**6.02 X 10**

23

OK, so maybe that makes sense why, but how the heck do you know what number to write in for the power?

That is what the whole rest of this lesson is about!

So, here we go...

**It must be a number between 1 - 10**

**So...**

**4.56 ??**

**Yes**

**45.6 ??**

**No**

**456.0 ??**

**No**

**6,593.32 ??**

**0.00125 ??**

**10.56 ??**

Count the number of places you must move the decimal to make a number between 1 - 10

**433,500,000**

1

2

3

4

5

6

7

8

We move the decimal eight

(8)

places

So, we raise the power on the 10 to ... eight

(8)

**4.335 X 10**

8

Try a few, with help.

Convert the following:

345.7 =

3.457 X 10

2

400,000 =

4.0 X 10

5

... and without help

23,000 =

143,000 =

809,000,000,000 =

5.76 X 10

=

5

576,000

2.3 X 10

3

=

2,300

9.86 X 10

=

7

??

6.5 X 10

=

14

??

OK, got some understanding there..

But, what about the really

small

numbers?

It is exactly the same as

BIG

numbers...

BUT....

Move the decimal the other way. Because we need to make a number...

Between

1 -10

, you knew that was coming, right?

So, here we go...

Rule #2

Count the number of places you need to move the decimal to make a number between 1 and 10.

0.00000000000012

1.2 is between 1 and 10

How many places?

1

2

3

4

5

6

7

8

9

10

11

12

13

13

places

so... That means...

1.2

X

10

-13

You try a few...

0.0097

=

9.7 X 10

-3

1

2

3

0.0000405

=

4.05 X 10

-5

0.058

=

??

0.000042

=

??

0.0000000000000000000031

=

??

So, how would you go from scientific notation back to a Standard notation number?

Pretty much the reverse of what we just did.

4.78 X 10

-5

=

Move

5

places

0.0000478

1

2

3

4

5

Try Some ...

3.9 X 10

-8

=

5.8 X 10

-12

=

??

??