Scientific Notation

Written by: James Wiens

Newton, Kansas

3.71 x 104 = 37,100

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

I. Warm-up: Exponents / moving decimal

II. Setting the Stage: Video lesson

III. Definitions / Key Concepts

IV. Guided practice: Turning Point Questions

V. Independent practice: Paper & pencil

VI. 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) -.0004

b) .0004

c) 10000

Setting the Stage

• There are 325,000 grains of sand in a tub. Write that number in scientific notation.

Answer

3.25 x 103

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 PracticeWrite in standard form:

A. 4.76 x 106 B. 6.21 x 103 C. 3.16 x 105

D. 2.71 x 108 E. 5.44 x 10-6 F. 3.54 x10-7

G. 4.32 x 10-4 H. 7.8 x 10-6 I. 7.8 x 10-1

Write in scientific notation:

J. 277,000 K. 523,000,000 L. 345,000,000

M. 654,000 N. 0.037 P. 0.0000767

Q. 0.00045 R. 0.00000232 S. 0.09004

Answer Key for Independent Practice

A. 4,760,000

B. 6,210

C. 316,000

D. 271,000,000

E. .000544

F. .000000354

G. .000432

H. .0000078

I. .78

J. 2.77 x 105

K. 5.23 x 108

L. 3.45 x 108

M. 6.54 x 105

N. 3.7 x 10-2

P. 7.67 x 10-5

Q. 4.5 x 10-4

R. 2.32 x 10-6

S. 9.004 x 10-2

Closure / Summary

• Explain why 32.8 x 104 is not correctly written in scientific notation.

• What does a negative exponent tell you about writing the number in standard form.

References

• Video Clip on Slide #11 is a link from the TeacherTube website which posted the video created by Studyzone.org

• Key concepts and definitions (slides 12-14) taken from Glencoe McGraw-Hill. Math connects cours 3. pages 130-131

• Remainder of lesson designed and written by James Wiens, 7th grade math teacher, Newton Kansas.