Scientific Notation

Scientific Notation 과학적 기수법

A short-hand way of writinglarge numbers without writing all of the zeros.

The Distance From the Sun to the Earth in miles

93,000,000

Step 1

Move decimal leftLeave only one number in front of decimal (one number to the left of the decimal).

Step 2

Write number without zeros

Step 3

Count how many places you moved decimalMake that your power of ten

The power often is 7 becausethe decimalmoved 7 places.

93,000,000 --- Standard Form (Decimal form)

9.3 x 107 --- Scientific Notation

Scientific notation

9.07 x 10 –

20.0907

5.06 x 10 –

40.000506

2.3 x 10122 300 000 000 000

1.27 x 102127

Scientific notationDecimal notation( 정수 )

Place Value Decimal System1 2 3 . 4 5 6 7

Millions

Hu

ndre

d T

ho

usand

s

Ten T

housands

Thousands

Hundreds

Tens

Ones

.T

enths

Hundredths

Thousandths

Ten

thousandths

Hu

ndre

d T

ho

usand

ths

Millionths

Ten M

illionths

106 105 104 103 102 101 100 10-1 10-2 10-3 10-4 10-5 10-6 10-7

100 20 3 0.4 0.05 0.006 0.0007

100 20 310

4

100

5

1000

6

10000

7

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.

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 = 3.48943 x 105

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

.0000000672 = 6.72 x 10-8

Page 82 Try changing these numbers to proper Scientific Notation:

1) 430

2) 3,400,000

3) 0.0000045

4) 11.2 x 104

5) 0.01 x 10-2

4.3 x 102

3.4 x 106

4.5 x 10-6

1.12 x 105

1 x 10-4

Rewrite these in decimal form Page 82

Multiplying with Scientific Notation

(5. X 102)(3.3 X 103)

• Multiply the Coefficients

• 5 X 3.3 = 16.5

• Add the Exponents

• 102 X 103 = 105

• 16.5 X 105

• BUT 16.5 is not greater than or equal to 1 and less than 10.

• so we must move the decimal place, 1.65 X 106

Practice Page 83 #1,2 Multiplying with Scientific

Notation

(2.2 X 10-2) X (3 X 105) =

(-3.2 X 105) X (2.1 X 102) =

6.6x103

-6.72x107

Dividing with Scientific Notation

• (3.3 X 104)/ (6.6 X 102)

• 3.3/ 6.6 = 0.5

• Subtract the Exponents

• 104 / 102 = 102

• 0.5 X 102

• BUT 0.5 is not greater than or equal to 1 and less than 10.

• 5 X 101

• (3.3 X 104)/ (2.3 X 102)

• 33000 / 230 = 143.4783

• Divide the Coefficients

• 3.3/ 2.3 = 1.434783

• Subtract the Exponents

• 104 / 102 = 102

• 1.4347823 X 102

• 143.4783

Dividing with Scientific Notation

(2.1 X 104) / (8.4 X 103) =

(3.1 X 103) / (6.2 X 105) =

2.5 x 100

5 x 10-3

Scientific Notation page 84 Addition/Subtraction

Homework

page 83 # 3-6page 84 all