Scientific Notation

Scientific Notation

Let’s face it: Numbers go to infinity.

TO INFINTY That 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”: 10000000000000000000000000000000000 0 00000000000000000000000000000000000 0 0000000000000000000000000

Wait, wait… How about one-google times three-google?

3000000000000000000000000000000 0000000000000000000000000000000 0000000000000000000000000000000 0000000000000000000000000000000 0000000000000000000000000000000 0000000000000000000000000000000 000000000000000

Wait, wait……what about really really small numbers? three-hundreths: .03 How about the OPPOSITE of google…”1 googlenth”:

0.0 0000000000000000000000000000000 0000000000000000000000000000000 0000000000000000000001

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 9 10 = 1000000000

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

4000000000 = 4 • 1000000000 Much easier !

=

4 • 10

9

Try some:

Scientific Notation ?

400000000000 = 4 • 100000000000 = 4 • 1011 3000000 =

3 • 1000000

= 3 • 106

200000000 =

2 • 100000000

= 2 • 108

34500000 =

345 • 100000

= 345 • 105

Scientific Notation involves a decimal number sometimes.

34500000 = 3.45 • 10000000

Calculate it !! That is 7 Scientific 3.45 • 10 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 • 10

13

What about really really small numbers ? It works the same way, except with negative integers.

.00000000000056

5.6 • 10

-13

“13 places”

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 Notation

It is easy to multiply scientific notation numbers. Por Ejemplo: Just multiply the numbers and 10’s separately

(2.34 • 10 )(4.5 • 10 ) 3

5

(2.34 • 4.5) (103 • 105)

(10.53 • 10 ) 9 8

Now put it in scientific notation

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) 5 3.45 10 • 4.5 106

.76 • 10 = = 7.6 • 10-2 -1