Alg 1 3-15-10

1.Get a calc and your keypad.2.Sit next to your assigned partner.3.Open up binders ready to take notes – binder

check.4.Formative Test this week – WED & FRI. – this is

the last one.5.EOC TEST 5/4/10!!!!!!!!!!!!!!!!!!!

SCIENTIFIC NOTATION

3.1432765654343636

0.0000005235

3.15 x 1011

3.15 x 1011

Learn to express large and small numbers in scientific notation.

23,345,345,678,554,561

0.00000000213

OUR SUN IS 93,000,000 MILES FROM EARTH.

How do you write this in scientific notation? 93,000,000

The Distance From the Sun to the Earth

93,000,000

Step 1

• Move decimal left• Leave only one number in front of decimal

Step 2

• Write number without zeros

Step 3

• Count how many places you moved decimal• Make that your power of ten

• 93,000,000 --- Standard Form

• 9.3 x 107 --- Scientific Notation

The speed of light is 186,000 miles per second.

What is the speed of light in miles per hour?

186000 mi per sec

x 3600 sec per hr

------------------669600000 mi per hr

669600000

6.696 x 108

At that speed, how far can light travel in one year?

669600000

669600000 mph

8760 hr per yr

------------------------------------5,865,696,000,000 mi per yr

5,868,324,000,000Over 5.8 trillion miles per year

Write in scientific notation.

5.868324 x1012

Write 28750.9 in scientific notation.

1. 2.87509 x 10-5

2. 2.87509 x 10-4

3. 2.87509 x 104

4. 2.87509 x 105

How wide is our universe?

210,000,000,000,000,000,000,000 miles(22 zeros)

This number is written in decimal notation. When numbers get this large, it is easier to write them in

scientific notation.

Scientific Notation

A number is expressed in scientific notation when it is in the form

a x 10n

where a is between 1 and 10and n is an integer

Write the width of the universe in scientific notation.

210,000,000,000,000,000,000,000 milesWhere is the decimal point now?

After the last zero.Where would you put the decimal to make

this number be between 1 and 10?Between the 2 and the 1

2.10,000,000,000,000,000,000,000.

How many decimal places did you move the decimal?

23When the original number is more than 1,

the exponent is positive.The answer in scientific notation is

2.1 x 1023

The nearest star to Earth (besides our sun) is Alpha Centauri.

It takes light 4.5 years to travel from Alpha Centauri

to Earth.

How many miles is it from Earth to Alpha Centauri?

4.5 x 5,865,696,000,000

26,395,632,000,000

2.6395632 x 1013

The fastest spacecraft ever built by man travels at

150,000 mph.

How long would it take to get to Alpha Centauri?

26,395,632,000,000 /150,000

26,395,632,000,000 / 150,000

175,970,880 hours

20,088 years

Write 531.42 x 105 in scientific notation.

1. .53142 x 102

2. 5.3142 x 103

3. 53.142 x 104

4. 531.42 x 105

5. 53.142 x 106

6. 5.3142 x 107

7. .53142 x 108

More Practice Problems

1) 734,000,000 = ______ x 108

2) 870,000,000,000 = ______x 1011

3) 90,000,000,000 = _____ x 1010

On these, decide where the decimal will be moved.

7.34 x 108

8.7 x 1011

9 x 1010

Complete Practice Problems

1) 50,0002) 7,200,0003) 802,000,000,000

Write in scientific notation.

5 x 104

7.2 x 106

8.02 x 1011

WHAT ABOUT SMALL NUMBERS?

1) Express 0.0000000902 in scientific notation.

Where would the decimal go to make the number be between 1 and 10?

9.02The decimal was moved how many places?

8When the original number is less than 1, the

exponent is negative.9.02 x 10-8

2) Express 1.8 x 10-4 in decimal notation.0.00018

3) Express 4.58 x 106 in decimal notation.4,580,000

On the graphing calculator, scientific notation is done with the button.

4.58 x 106 is typed 4.58 6

4) Use a calculator to evaluate: 4.5 x 10-5

1.6 x 10-2

Type 4.5 -5 1.6 -2

You must include parentheses if you don’t use those buttons!!

(4.5 x 10 -5) (1.6 x 10 -2)

0.0028125Write in scientific notation.

2.8125 x 10-3

5) Use a calculator to evaluate: 7.2 x 10-9

1.2 x 102

On the calculator, the answer is:6.E -11

The answer in scientific notation is 6 x 10 -11

The answer in decimal notation is 0.00000000006

6) Use a calculator to evaluate (0.0042)(330,000).

On the calculator, the answer is1386.

The answer in decimal notation is 1386

The answer in scientific notation is 1.386 x 103

7) Use a calculator to evaluate (3,600,000,000)(23).

On the calculator, the answer is:8.28 E +10

The answer in scientific notation is 8.28 x 10 10

The answer in decimal notation is 82,800,000,000

Write (2.8 x 103)(5.1 x 10-7) in scientific notation.

1. 14.28 x 10-4

2. 1.428 x 10-3

3. 14.28 x 1010

4. 1.428 x 1011

Write in PROPER scientific notation.(Notice the number is not between 1 and 10)

8) 234.6 x 109

2.346 x 1011

9) 0.0642 x 104

on calculator: 6426.42 x 10 2

The power often is 7 becausethe decimalmoved 7 places.

Practice Problem

1) 98,500,000 = 9.85 x 10?

2) 64,100,000,000 = 6.41 x 10?

3) 279,000,000 = 2.79 x 10?

4) 4,200,000 = 4.2 x 10?

Write in scientific notation. Decide the power of ten.

9.85 x 107

6.41 x 1010

2.79 x 108

4.2 x 106

Scientific Notation to Standard Form

Move the decimal to the right

3.4 x 105 in scientific notation

340,000 in standard form

3.40000 --- move the decimal

Write in Standard Form

• 6.27 x 106

• 9.01 x 104

• 6,270,000• 90,100