Scientific Notation

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

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

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

Complete Practice Problems

1) 50,000

2) 7,200,000

3) 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

Positive Exponents

101 = 10

102 = 10X10= 100

103 = 10X10X10 = 1000

104 = 10X10X10X10 = 10,000

Negative Exponents

10-1 = 1/10 = 0.1

10-2 = 1/100 = 0.01

10-3 = 1/1000 = 0.001

10-4 = 1/10000 = 0.0001

Scientific Notation

We use the idea of exponents to make it easier to work with large and small numbers.

10,000 = 1 X 104

250,000 = 2.5 X 105

Count places to the left until there is one number to the left of the decimal point.

230,000 = ?

35,000 = ?

Scientific Notation Continued

0.00006 = 6 X 10-5

0.00045 = 4.5 X 10-4

Count places to the right until there is one number to the left of the decimal point

0.003 = ?

0.0000025 = ?

Multiplying with Scientific Notation

Add the Exponents

102 X 103 = 105

100 X 1000 = 100,000

Multiplying with Scientific Notation

(2.3 X 102)(3.3 X 103)

• 230 X 3300

• Multiply the Coefficients

• 2.3 X 3.3 = 7.59

• Add the Exponents

• 102 X 103 = 105

• 7.59 X 105

• 759,000

Multiplying with Scientific Notation

(4.6 X 104) X (5.5 X 103) = ?

(3.1 X 103) X (4.2 X 105) = ?

Dividing with Scientific Notation

Subtract the Exponents

104/103 = 101

10000X 1000 = 10

Dividing with Scientific Notation

(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

(4.6 X 104) / (5.5 X 103) = ?

(3.1 X 103) / (4.2 X 105) = ?

Addition and subtractionScientific Notation

1. Make exponents of 10 the same2. Add 0.2 + 3 and keep the 103 intact

The key to adding or subtracting numbers in Scientific Notation is to make sure the exponents are the same.

2.0 x 102 + 3.0 x 103

.2 x 103 + 3.0 x 103

= .2+3 x 103

= 3.2 x 103

2.0 x 107 - 6.3 x 105

2.0 x 107 -.063 x 107

= 2.0-.063 x 107

= 1.937 x 107

1. Make exponents of 10 the same2. Subtract 2.0 - .063 and keep the 107 intact