Scientific Notation
Terry Scates
Newton, Kansas
Instructor Notes• Subject Area(s): Math
• Grade level: 7th grade
• Lesson Length: 50 minute class period
• Synopsis: Use scientific notation to write very large and very small numbers.
• Objective/goals: Students will change numbers from standard form into scientific notation and from scientific notation back into standard form.
• Standard: ▲equivalent representations of rational numbers and simple algebraic expressions, e.g., you are in the mountains. Wilson Mountain has an altitude of 5.28 x 103 feet. Rush Mountain is 4,300 feet tall. How much higher is Wilson Mountain than Rush Mountain? (KS standard 7.1.1.A1a)
• Pre-requisite skills: Vocabulary – Standard form, Scientific notation, exponent, base number.
• TurningPoint functions: standard question slides
• Materials: All instructional points and practice problems are provided within the power point slides. Practice questions are designed to be used with the TurningPoint clickers.
Instructor Notes
Lesson Outline
1. Warm-up: Exponents / moving decimal
2. Setting the Stage: Powers of Ten Diagram
3. Definitions / Key Concepts
4. Guided practice: Turning Point Questions
5. Independent practice: Paper & pencil
6. Closure: Write about scientific notation
Write each power of ten in standard notation.
0%
100%
0%
103
a) 30
b) 100
c) 1000
Write each power of ten in standard notation.
33% 33%33%
106
a) 60
b) 1000000
c) 10000
Write each power of ten in standard notation.
33% 33%33%
10-2
a) .01
b) -20
c) 100
Write each power of ten in standard notation.
33% 33%33%
10-4
a) -.0001
b) .0001
c) 10000
Power of Ten in Standard Notation101 = 10 10-1 = .1
102 = 100 10-2 = .01
103 = 1,000 10-3 = .001
104 = 10,000 10-4 = .0001
105 = 100,000 10-5 = .00001
106 = 1,000,000 10-6 = .000001
107 = 10,000,000 10-7 = .0000001
108 = 100,000,000 10-8 = .00000001
109 = 1,000,000,000 10-9 = .000000001
Changing Numbers From
Standard Form to
Scientific Notation
4.075 x 10,000,000 = 40,750,000 (standard form)
4.075 x 107 (scientific notation)
Move the decimal point 7 places to the right.
4.075_ _ _ _ (add zeros to blank spaces)
40,750,000
Changing Numbers From
Standard Form to
Scientific Notation
3.2 x 0.0001 = 0.00032 (standard form)
3.2 x 10-4
(scientific notation)
Move the decimal point 4 places to the left.
_ _ _ 3.2(put zeros in the blank spaces)
0.00032
Setting the Stage
• There are 325,000 grains of sand in this tub.
• Write that number in scientific notation.
Answer
325,000 = 3.25 x 105
.
Video Clip Lesson from Teacher Tube
• Click on the link at the right to access a lesson about scientific notation from Teacher Tube.
Click here to see the lesson
Definition
• Scientific notation is a compact way of writing numbers with absolute values that are very large or very small.
• Glencoe McGraw-Hill. Math connects cours 3. pages 130-131
Scientific notation to Standard Form
• Multiplying by a positive power of 10 moves the decimal place to the right.
• Multiplying by a negative power of 10 moves the decimal place to the left.
• The number of places the decimal point moves is the absolute value of the exponent.
• Glencoe McGraw-Hill. Math connects cours 3. pages 130-131
Standard Form to Scientific Notation
• Move the decimal point to the right of the first nonzero digit.
• Count the number of places you moved the decimal point.
• Find the power of 10. If the absolute value of the original number was between 0 and 1, the exponent is negative. Otherwise, the exponent is positive.
• Glencoe McGraw-Hill. Math connects cours 3. pages 130-131
What is 2.85 x 104 written in standard form?
A. .000285
B. 285
C. 28500
D. 2850
What is 3.085 x 107 written in standard form?
A. .0000003085
B. 30,850,000
C. 3085
D. 308,500,000
What is 1.55 x 10-3 written in standard form?
A. .00155
B. 155
C. 1550
D. .000155
What is 2.7005 x 10-2 written in standard form?
A. 270.05
B. 27005
C. .27005
D. .027005
Independent Practice Write in standard form:
A. 4.76 x 106
B. 6.21 x 103
C. 3.16 x 105
D. 5.44 x 10-6
E. 4.32 x 10-4
F. 7.8 x 10-6
Independent Practice Answer Key
A. 4,760,000
B. 6,210
C. 316,000
D. .00000544
E. .000432
F. .0000078
Closure / Summary
What does a negative exponent tell you about writing the number in standard form?
References
• Glencoe McGraw-Hill Math Connects Course 2, Textbook, 2008
• TeacherTube website which posted the video created by Studyzone.org
• Wiens, James, Standard Notation, PowerPoint presentation, 2008.