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.