Scientific Notation

They encounter really BIG numbers like...

300,000,000,000,000,000,000,000,000,000,000 kg

or

They encounter really SMALL numbers like...

0.000000000000000000000000030 kg

Both of these examples

300,000,000,000,000,000,000,000,000,000,000 kg

and

0.000000000000000000000000030 kg

are written in Standard Notation

(it's the way we write numbers all the time)

So they come up with a more convenient way to write really BIG numbers or really small numbers.

It's called Scientific Notation.

Scientific Notation DOES NOT change the value of the number. Just makes it easier to write.

Scientific Notation uses Powers of 10.

Have a base of 10 and an exponent

Examples:

10¹ = 10 

10² = 10 x 10 = 100

10³ = 10 x 10 x 10 = 1,000

10⁴ = 10 x 10 x 10 x 10 = 10,000

10⁵ = 10 x 10 x 10 x 10 x 10 = 100,000

ALWAYS in a specific form

#.# x 10^#

Example: 2.3 x 10¹²

Video to help you if you are walking through this lesson on your own.

6.5 X 10⁶ = 6.5 x 1,000,000 = 6,500,000

SHORTCUT: if the exponent is positive, move the decimal that many places to the right.

6.5 X 10⁶

the 6 is positive to six places to the right.

Video to help you if you are walking through this lesson on your own.

The example is a BIG number.

What I would add is...

Since its a BIG number, my exponent will be positive.

The example is a SMALL number.

What I would add is...

Since its a SMALL number, my exponent will be negative.