Scientific Notation

Let’s face it: Numbers go to infinity.

TO INFINTYThat way

…and it is a pain in the butt to write out really really really big numbers.

“One Trillion”:

1,000,000,000,000

“One Google”:

100000000000000000000000000000000000

000000000000000000000000000000000000

0000000000000000000000000

Wait, wait…

How about one-google times three-google?

300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Wait, wait……what about really really small numbers?

three-hundreths: .03

How about the OPPOSITE of google…”1 googlenth”:

000000000000000000000000000000000000000000000000000000000000000000000000000000000001

0.0

Have no fear!!!

We have EXPONENTS to help us out!

SCIENTIFIC NOTATION: a way to write really large numbers without hurting your hand.Try these in your calculator:

103 104 105 109

103 = 1000

104 = 10000

105 = 100000

109 = 1000000000

Scientific Notation is taking any number and multiplying it by 10 with an exponent.

4000000000 = 4 • 1000000000

= 4 • 109Mucheasier

!

Try some:

400000000000 =

3000000 =

200000000 =

34500000 =

4 • 100000000000

3 • 1000000

2 • 100000000

345 • 100000

= 4 • 1011

= 3 • 106

= 2 • 108

= 345 • 105

Scientific Notation ?

Scientific Notation involves a decimal number sometimes.

34500000 = 3.45 • 10000000

Calculate it !!

3.45 • 107That isScientific Notation !

How to do it.Count how many places you move the

decimal until you get next to the last digit.

45600000000000

That is your power of 10

Now put a decimal next to the number, and write any other non-zero numbers, and times it by the power of ten you counted.

4.56 • 1013

What about really really small numbers ?

It works the same way, except with negative integers.

.00000000000056 “13 places”

5.6 • 10 -13

REVIEW

To change numbers from scientific notation to regular ….

if the power of ten is positive, just move the decimal to the left to make it a big number.

if the power of ten in negative, just move the decimal to the right to make it a really small number.

Multiplying Scientific NotationIt is easy to multiply scientific notation

numbers.

Por Ejemplo:

(2.34 • 103)(4.5 • 105)

Just multiply the numbersand 10’s separately

(2.34 • 4.5)

(10 53 • 10 )Now put it in scientific notation. 89

(103 • 105)

Try it in your calculator:

Type in :

.00000000000056

then hit enter….

When dividing them, just divide the numbers and ten’s separately:

(3.45 • 105)

(4.5 • 106)

3.454.5

• 105

106

.76 • 10-1=

7.6 • 10-2=