Scientific Notation

Why use scientific notation?

For very large and very small numbers, these numbers can be converted into scientific notation to express them in a more concise form.

Numbers expressed in scientific notation can be used in a computation with far greater ease.

Scientific notation consists of two parts:

A number between 1 and 10

A power of 10

N x 10x

What is scientific Notation?A method to write very large or

very small numbers

Coefficient – any number from 1-9

Exponent – shows the number of times 10’s are multiplied together (102 = 10 x 10 = 100)

Changing standard form to scientific notation.

Changing Standard Numbers to Scientific Notation

1. Numbers greater than 10

a. Move decimal until only ONE number is to the left of the decimal.

b. The exponent is the number of places the decimal has moved and it is POSITIVE.

Ex. 125 =

15,000,000,000 =

1.25 102

1.5 1010

2. Numbers less than 1

a. Move decimal until only one number is to the left of the decimal.

b. The exponent is the number of places the decimal has moved and it is NEGATIVE.

Ex. 0.000189 =

0.5476 =

Changing Standard Numbers to Scientific Notation, cont.

1.89 10-4

5.476 10-1

Example 1

Given: 289,800,000Use: 2.898 (moved 8

places)Answer: 2.898 x 108

Example 2

Given: 0.000567Use: 5.67 (moved 4 places)

Answer: 5.67 x 10-4

3. To change a number written in incorrect scientific notation:

a. Move the decimal until only one number is to the left of the decimal.

b. Correct the exponent. (remember: take away, add back)

Ex. 504.2 106 =

0.0089 10-2 =

Changing Standard Numbers to Scientific Notation, cont.

5.042 108

8.9 10-5

Changing scientific notation to standard form.

To change scientific notation to standard form…

Simply move the decimal point to the right for positive exponent 10.

Move the decimal point to the left for negative exponent 10.

(Use zeros to fill in places.)

Changing Numbers in Scientific Notation to Standard Notation

1. If the exponent is (+) move the decimal to the right the same number of places as the exponent.

a. 1.65 101 = b. 1.65 103 =

2. If the exponent is (-) move the decimal to the left the same number of places as the exponent.

a. 4.6 10-2 = b. 1.23 10-3 =

16.51650

0.046

0.00123

Example 3

Given: 5.093 x 106

Answer: 5,093,000 (moved 6 places to the right)

Example 4

Given: 1.976 x 10-4

Answer: 0.0001976 (moved 4 places to the left)

Even More Practice

Below is a list of links to games and activities all having to do with scientific notation.– http://www.aaamath.com/dec71i-dec2sci.ht

ml– http://janus.astro.umd.edu/cgi-bin/astro/sci

note.pl– http://www.sciencejoywagon.com/physicsz

one/lesson/00genral/dectosci.htm