Scientific Notation

Scientific Notation

4.632 x 106

Coefficient is 4.632

Baseis 10

Exponent is 6

IMPORTANT RULES

The coefficient is always larger than or equal to 1, and smaller than 10.

The base is always 10.

The exponent is positive for large numbers, and negative for numbers less than 1. The exponent can not be a decimal (like 3.5)

4.632 x 106

Take note

• Negative numbers are not written in scientific notation.

• When the exponent on the base is negative (when a number is written in scientific notation), that means the number is between 0 and 1.

4.632 x 10-6 This number is between 0 and 1

Why use Scientific Notation?

• The speed of light is 300,000,000 m/sec

• The speed of light is often represented by the letter c.

• It is a large number used in many calculations (E = mc2)

• In scientific notation it is written 3.0 x 108

• It is easier to calculate with large numbers in scientific notation.

How does Scientific Notation Work?

• 14 0,000,000,000 standard form

• 1.4 x 10?

• 1.4 x 1011 scientific notation

What number goes here?

Scientific Notation: Great for very small numbers

• The size of a dust particle is about 0.000 000 000 752 kilograms

• 0.000 000 000 752 standard form

• 7.52 x 10?

• 7.52 x 10-10 scientific notation

What does Scientific Notation look like on the HP 39G ?

Find the EEX key

To access these second functions, you need to hit the SHIFT key

Using the HP 39 G

• Enter the following number:

• 3.4 x 1011

• 3.4 shift EEX 11 enter

• Notice that both the scientific form and the standard form are displayed on the screen

Using the HP 39 G

• Enter the following number:

• 2.46 x 10-9

• 2.46 SHIFT EEX (-) 9

The sun is about (1.5 x 1011) meters from the earth. Light travels at approximately (3.0 x 108) meter/sec. How many seconds does it take for light to travel from the sun to the earth? (distance = speed x time)

a) 50 seconds

b) 5.0 x 102 seconds

c) 5.0 x 103 seconds

Answer is b.

Do example 6 now

• A space ship is 25,000,000,000 from Earth. How long would it take the space ship to reach Earth if it flew 550 miles/hr the whole way?

distance = (speed)(time)

• 25,000,000,000 = (550) (t) [put calculator in scientific mode]

• t = 4.55 x 107

Thiomargarita namibiensis is the largest known species of bacteria and is approximately 7.5 x 10-4 m wide. The average bacterium is about the size of Escherichia coli and is about 1.5 x 10-6 m wide. What is the difference in widths of the two species?

a) 74.9 x 103 mb) 7.5 x 10-1 mc) 7.5 x 10-4 m

E. coli

T. namibiensisAnswer is c.

Solve and express the answer in scientific notation:

( 2.45 x 105 ) x (5 x 103 )

a) 1.225 x 109

b) 12.25 x 108

c) 1.225 x 1015

d) 12.25 x 1015

Answer is a

Do example 5 now

Multiply the following numbers. Express your answer in scientific notation.

(3.4 x 105) x ( 4.8 x 107)

calculator emulator

Answer is 1.632 x 1013

Degree of accuracy

• What is the degree of accuracy for the number 854. 4463 ?

• The 3 is in the 10,000ths place so the degree of accuracy is 1/10,000