U2L1 ­ Powers of Ten and Scientific Notation.notebook
November 01, 2016
Date: _________________________________
Unit 2: Exponents and Radicals
Lesson 1: Powers of Ten and Scientific Notation
WARM-UP:
1 billion dollars is a lot of money! Write 1 billion in 3 ways:
Clearly, it is much easier to write such a large number in exponential form! 1
U2L1 ­ Powers of Ten and Scientific Notation.notebook
November 01, 2016
Powers always have a base and an exponent.
The base can be a number, or just a variable, or a
combination of things.
Here are a few examples of powers:
Recall: x2 is read as "x squared" and x3 is read as "x cubed"
Discuss: is 2y6 equal to (2y)6
Recall:
…. 10-4
10-3
10-2
10-1
100
101
102
103
104…
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U2L1 ­ Powers of Ten and Scientific Notation.notebook
November 01, 2016
Scientific Notation
• Scientific Notation is used when writing very small or
very large numbers that contain many zeros.
• In scientific notation, a number is written in the form:
where
• Large numbers have positive exponents and small
numbers have negative exponents.
Examples:
Complete the following tables:
3
U2L1 ­ Powers of Ten and Scientific Notation.notebook
November 01, 2016
Scientific Notation
• Scientific Notation is used when writing very small or very large
numbers that contain many zeros.
• In scientific notation, a number is written in the form:
where
• Large numbers have positive exponents and small numbers have
negative exponents.
Examples:
Complete the following tables:
4
U2L1 ­ Powers of Ten and Scientific Notation.notebook
November 01, 2016
Practice:
1) Write each of the following numbers in scientific notation:
a) 3 200 b) 0.000 058 c) 780 000 d) 0.000 000 007
2) Write each of the following numbers in standard form:
a) 5.6 x 102
c) 3.99 x 10­2
3)
b) 2.98 x 10­4
d) 8.57 x 105
a) Explain why 102 x 106 is not in scientific notation.
b) Rewrite this number in scientific notation.
4) Evaluate the following. Express your answer in scientific
notation.
a) (4.5 x 103) (2.1 x 102) b) (5.5 x 108) (3.2 x 10­4)
c) (5.5 x 10­2) (3.4 x 105) 5
U2L1 ­ Powers of Ten and Scientific Notation.notebook
November 01, 2016
Practice:
1) Write each of the following numbers in scientific notation:
a) 3200
b) 0.000058
c) 780 000
d) 0.000000007
= 3.2 x 103
= 5.8 x 10-5
= 7.8 x 105
= 7 x 10-9
2) Write each of the following numbers in standard form:
a) 5.6 x 102
= 560
b) 2.98 x 10­4
= 0.000 298
c) 3.99 x 10­2
d) 8.57 x 105
= 0.0399
= 857 000
3)
a) Explain why 102 x 106 is not in scientific notation. b) Rewrite this number in scientific notation.
6
U2L1 ­ Powers of Ten and Scientific Notation.notebook
4)
November 01, 2016
Evaluate the following. Express your answer in scientific notation.
a) (4.5 x 103) (2.1 x 102)
b) (5.5 x 108) (3.2 x 10­4)
c) (5.5 x 10­2) (3.4 x 105)
= 18.7 x 103
= 1.87 x 104
7
U2L1 ­ Powers of Ten and Scientific Notation.notebook
November 01, 2016
Assigned Work
Complete
Worksheet!
8
U2L1 ­ Powers of Ten and Scientific Notation.notebook
November 01, 2016
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