large numbers 1,000 x 1 thousand = 1 million (10 6 ) 1,000 x 1 million = 1 billion (10 9 ) 1,000 x 1...

Large Numbers• 1,000 X 1 thousand = 1 million (106) 

1,000 X 1 million = 1 billion (109) 1,000 X 1 billion = 1 trillion (1012) 1,000 X 1 trillion = 1 quadrillion (1015) 1,000 X 1 quadrillion =1 quintillion(1018) 1,000 X 1 quintillion = 1 sextillion (1021) 

Large Numbers1,000 X 1 sextillion =1 septillion (1024) 1,000 X 1 septillion =1 octillion (1027) 1,000 X 1 octillion = 1 nonillion (1030) 1,000 X 1 nonillion = 1 decillion (1033) 1,000 X 1 decillion = 1 undecillion (1036)1,000 X 1 undecillion =1 duodecillion

(1039) 

•One googol = 10100 One googolplex = 10googol One googolplexian = 10googolplex 

People in the US eat approximately 1,120,000,000 pounds of popcorn a year. Write this number in Scientific Notation.

EXIT Ticket

Scientific Notation

VOCABULARY

• scientific notation • exponential notation• standard form base• Factor power• Exponent decimal• place value positive

number• negative number

OBJECTIVE

•The students will be able to represent rational numbers by using scientific notation.

•rational numbers= whole numbers and decimal numbers

Powers of 10

• 105 =• 104 =• 103 =• 102 =• 101 =

• 100 =

Powers of 10

• 10-5 =• 10-4 =• 10-3 =• 10-2 =• 10-1 =

Scientific Notation

-used to represent large and small numbers -it is made up of two factors: the first is greater than or equal to 1 and less than 10; and the second is a power of ten. .

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

The power often is 7 becausethe decimalmoved 7 places.

•93,000,000 --- Standard Form

•9.3 x 107 --- Scientific Notation

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 in Word Problems

1. There are over 300,000,000,000 stars in the Andromeda Galaxy. Write the number of stars in scientific notation.

Scientific Notation in Word Problems

2. There are approximately 306,000,000 people in United States of America. Write the population in the US in scientific notation.

Scientific Notation in Word Problems

3. The current population in the world is about 6.9 billion. Write the population in scientific notation.

Scientific Notation in Word Problems

4. The thickness of a soap bubble is about 0.000004 meter. What is the thickness of the soap bubble written in scientific notation?

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.

1) 7.34 x 108 2) 8.7 x 1011 3) 9 x 1010

Practice Problems

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

Write in scientific notation.

1) 5 x 104 2) 7.2 x 106 3) 8.02 x 1011

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

When using Scientific Notation, there are two kinds of exponents: positive and negative

Positive Exponent:

2.35 x 108

Negative Exponent:

3.97 x 10-

7

When changing scientific notation to standard notation, the exponent tells you if you should move the decimal:

With a positive exponent, move the decimal to the right:

4.08 x 103 = 4 0 8

Don’t forget to fill in your zeroes!

When changing scientific notation to standard notation, the exponent tells you if you should move the decimal:

With a negative exponent, move the decimal to the left:

4.08 x 10-3 = 4 0 8

Don’t forget to fill in your zeroes!

An easy way to remember this is:

• If an exponent is positive, the number gets larger, so move the decimal to the right.

• If an exponent is negative, the number gets smaller, so move the decimal to the left.

The exponent also tells how many spaces to move the decimal:

4.08 x 103 = 4 0 8 In this problem, the exponent is +3, so the decimal moves 3 spaces to the right.

The exponent also tells how many spaces to move the decimal:

4.08 x 10-3 = 4 0 8

In this problem, the exponent is -3, so the decimal moves 3 spaces to the left.

Try changing these numbers from Scientific Notation to Standard Notation:

1) 9.678 x 104

2) 7.4521 x 10-3

3) 8.513904567 x 107

4) 4.09748 x 10-5

96780

.0074521

85139045.67

.0000409748

When changing from Standard Notation to Scientific Notation:

1) First, move the decimal after the first whole number:

3 2 5 8

123

3

2) Second, add your multiplication sign and your base (10).

3 . 2 5 8 x 10

3) Count how many spaces the decimal moved and this is the exponent. 3 . 2 5 8 x 10

When changing from Standard Notation to Scientific Notation:

4) See if the original number is greater than or less than one.– If the number is greater than one, the

exponent will be positive.

348943 = 3.489 x 105

– If the number is less than one, the exponent will be negative.

.0000000672 = 6.72 x 10-8

Try changing these numbers from Standard Notation to Scientific Notation:

1) 9872432

2) .0000345

3) .08376

4) 5673

9.872432 x 106

3.45 x 10-5

8.376 x 102

5.673 x 103