Download Math 35 Introduction

Section 1.7
Scientific Notation




Powers of 10 Review
Converting Numbers to Scientific Notation
Converting Numbers from Scientific Notation
Simplifying Computations
1.7
1
Powers of 10 - Review

Change to standard notation:











102 = 100
103 = 1000
106 = 1,000,000
10n = 100,000 What is n? n = 5
10-1 = 0.1
10-2 = 0.01
10-7 = 0.0000001
10m = 0.00001 What is m? m = -5
103 • 106 = 103+6 = 109
103 ÷ 107 = 103-7 = 10-4
1.7
4
-4
4+(-4)
0
10 • 10 = 10
= 10 = 1 important!
2
Scientific Notation
For correct Scientific Notation,
a single non-0 digit must
precede the decimal point.
1.7
3
Examples – Move the Decimal Point
4 positions – small number  5.17 × 10-4
8 positions – big number  5.23 × 108
1.7
4
Examples – Converting & Computing
689300000000
689,300,000,000
Add 8 zeros (total 11 places)
Put in commas from right
= 1.12 • 5 • 10-8 • 10-7
= 5.6 x 10-15
1.7
5
Adjusting to Correct Scientific Notation









Correct format is M × 10n where 1 ≤ M < 10
Good Examples: 3.2 × 102 9.999 × 10-4 106
Wanna Be’s:
432 × 103 Incorrect Format
4.32×102×103 Convert 432 to Sci Not
4.32 × 105 Add the exponents
0.00234 × 10-7 Incorrect Format
2.34×10-3×10-7 Convert 0.00234 to Sci Not
2.34 × 10-10 Add the exponents
1.7
6
Rounding Products & Quotients
1.7
7
Simplifying Multiplication and
Division Using Scientific Notation
4.0 × 10-3
2.1 × 102
2 × 1016
1.4 × 107
1.7
8
What Next?

2.1 – Graphs
1.7
9