Download Section 2.2

Chapter 2.2
Scientific Notation
Scientific Notation
• Expresses numbers in two parts:
• A number between 1 and 10
• Ten raised to a power
• Examples:
• 2.32 x 102
• 1.767 x 10-12
Interpreting Scientific Notation
• When the power of ten is positive, than the
number is larger than 1
• Move the decimal to the right
• Examples:
• 4.56 x 103 = 4,560
• 1.2 x 105 = 120,000
• 6.8 x 102 = 680
Interpreting Scientific Notation
• When the power of ten is negative, than the
number is smaller than 1
• Move the decimal to the left
• Examples:
• 5.23 x 10-3 = 0.00523
• 2.03 x 10-2 = 0.0203
• 7 x 10-5 = 0.000007
Converting Data into Scientific
Notation
• Move the decimal to produce a factor between
1 and 10
• Count the number of places the decimal moved
and in what direction
• If it moved to the left, express the exponent as a
positive number
• If it moved to the right, express the exponent as
a negative number
Example
2,345,000
Expressed as a factor between 1 and 10:
2.345
Decimal moved 6 places to the left:
2.345 x 106
Example
0.00178
Expressed as a factor between 1 and 10:
1.78
Decimal moved 3 places to the right:
1.78 x 10-3
Adding and Subtracting
• Only add and subtract numbers with the same
exponent
• Convert numbers to the same power of ten
before adding or subtracting
6 x 102 + 3 x 103 = 6 x 102 + 30 x 102
= 36 x 102
= 3.6 x 103
Multiplying and Dividing
• The numbers do not have to have the same
exponent
• For multiplying: Multiply the first factors, then
add the exponents
• For dividing: Divide the first factors, than
subtract the exponent of the divisor from the
exponent of the dividend
Multiplication Example
(4 x 103) x (2 x 104)
Multiply the first factors
4 x 2= 8
Add the exponents
3+4=7
Combine the factors
8 x 107
Division Example
(15 x 103) ÷ (3 x 10-4)
Divide the first factors
15 ÷ 3 = 5
Subtract the exponents
3 – (-4) = 7
Combine the factors
5 x 107
Homework
• Practice problems 12-21 on pages 32-35