The focus of this lesson is changing numbers from standard form to scientific notation.
Scientific notation has three parts to it: the coefficient, the base, and the exponent.
exponent
1.23 X
coefficient
104
base
VOCABULARY
Standard Form
The way a number is written “normally”, for example 1,342,007 or 0.0326.
Notation
A system of numbers or symbols used instead of letters and words. Musical
notes are a form of notation.
Coefficient
The number used to multiply 10 to a certain power. The coefficient must be
greater than 1 and less than 10.
Base
Exponent
The base is always 10.
The number of places the decimal was moved to obtain the coefficient.
LESSON DESCRIPTION
Materials: Student Recording Sheet
1. Students work as a group on the warm-up activity to gain perspective on large numbers.
2. Next, discuss when scientific notation is used (to write very large or very small numbers instead of
writing lots and lots of zeroes), and the proper format for scientific notation (see above).
3. Students work on the problems. If there is extra time, do the challenge problem.
1
Scientific Notation
Student Recording Sheet
Name ______________________________________________________
Date _________________
1. The mass of an electron is 9.11 x 10-31 kg. What is the coefficient? 9.11
What is the exponent? -31
2. Complete the table
Place Value
Number
Expanded Form
Scientific Notation
Millions
7,000,000
7 x 1,000,000
7 x 106
Hundred Thousands
700,000
7 x 100,000
7 x 105
Ten Thousands
70,000
7 x 10,000
7 x 104
Thousands
7,000
7 x 1,000
7 x 103
Hundreds
700
7 x 100
7 x 102
Tens
70
7 x 10
7 x 101
Ones
7
7x1
7 x 100
Tenths
.7
7 x .1
7 x 10-1
Hundredths
.07
7 x .01
7 x 10-2
Thousandths
.007
7 x .001
7 x 10-3
Ten-thousandths
.0007
7 x .0001
7 x 10-4
Hundred-thousandths .00007
7 x .00001
7 x 10-5
Millionths
7 x .000001
7 x 10-6
.000007
3. Fill in each blank with the word POSITIVE or NEGATIVE.
A. Large numbers have positive exponents.
B. Small numbers have negative exponents.
C. Would the exponent for the power of ten be positive or negative for these numbers
when written in scientific notation?
i. 589,000,000,000 positive
i. 18 positive
iii. 0.000000123 negative
iv. 0.07 negative
4. What is your age in years in scientific notation? For example, 29 is written as 2.9 x 101.
5. How many seconds are there in an hour? How many in a day? Write these in scientific notation.
A. Seconds in an hour? 3.6 x 10 3
B. Seconds in a day? 8.64 x 10 4
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Scientific Notation
Student Recording Sheet
6. A new star was found 1,234,000,000,000,000 miles from the moon. How is this number
rewritten in Scientific Notation?
A. 12.34 X 1014
B. 1.234 X 1015
C. 1.234 x 1012
D. 12.34 x 1012
7. Human hair grows at about the rate of 1 x 10-8 miles per hour. How is this number
rewritten in Scientific Notation?
A. 0.00000001
B. 0.0000001
C. 0.00000010
D. 1.0000000
8. Is 19.625 x 105 written in scientific notation? Why or why not? The number is not written in
scientific notation because the coefficient must be greater than 1 and less than 10. The
coefficient in this example is greater than 10.
9. Rewrite the following numbers in standard notation.
A. 3 x 100 3
B. –7 x 101 -70
C. –6 x 10-3 -.006
D. 5 x 106
5000000
10. Place the >, <, or = in each blank.
A. 8.12 x 1015 > 1.5 x 1017
B. 2.33 x 1010 < 7.6 x 1010
C. 4.4 x 107
=
44,000,000
D. 548,000,000 > 5.48 x 107
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Scientific Notation
TEKS:
8.1 Number, operation, and quantitative reasoning. The student understands that
different forms of numbers are appropriate for different situations. The student
is expected to
(D) express numbers in scientific notation, including negative exponents, in
appropriate problem situations.
Modification Ideas:



Review vocabulary with students, particularly exponent, coefficient, and base.
Do Problem #2 slowly and as a group. Encourage the students to identify any
patterns while completing the table. Refer to the table when answering
subsequent questions.
Students may also benefit from using a sentence stem as support when
discussing writing in scientific notation. Model the use and then have students
say: “I moved my decimal point _____ places to the _____ because ___________.
Extension Ideas:

Select a Challenge Question after the Evaluation questions and work as a group to
solve the problem.

Have your students convert 1 million (and billion and trillion) minutes to days and
years (see “How Much is a Billion” on page 6).
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Scientific Notation
Evaluation
Name ______________________________________________________
Date _________________
1.
A certain bacterium measures approximately 0.000015 millimeter in length. How is this
length expressed in scientific notation?
F.
G.
H.
J.
2.
1.5 x 10-5 mm
1.5 x 10-4 mm
0.15 x 105 mm
15 x 10-4 mm
Mr. Loya stated that the circumference of Earth at the equator is 24,902.4 miles. Which
expression represents this number in scientific notation?
A. 2.49024 × 10 4
B. 24.9024 × 10 4
C. 249.024 × 10 4
D.
3.
2.49024 × 10 5
The average distance from Earth to the sun is about 9.3 x 107 miles. The average distance
from Mars to the sun is about 1.4 x 108 miles. When both planets are at their average
distance from the sun, how much farther is Mars from the sun than Earth?
A 79,000,000 mi
B 47,000,000 mi
C 107,000,000 mi
D
233,000,000 mi
Answers
1.F
2.A
3.B
CHALLENGE PROBLEM
The average person’s heart beats 70 times per minute. Estimate how many times your heart
has beaten during your lifetime. Do not worry about leap years. Express your answer in
scientific notation.
70 beats/min * 60 mins = 4,200 beats/hr
4,200 beats/hr * 24 hrs = 100,800 beats/day
100,800 beats/day * 365 days = 36,792,000 beats/year
36,792,000 beats/yr * 13 yrs = 478,296,000 beats in 13 years
= 4.78296 x 108
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Scientific Notation
Bonus Problem
Name ______________________________________________________
Date _________________
How Much is a Billion?
How much is a million? How big is a billion? How much more is a trillion than a million?
To understand the difference between one million and one trillion, calculate
a) how many days/years one million minutes is;
b) how many years one billion minutes is; and
c) how many years one trillion minutes is.
a.
b.
c.
1 million minutes x
1 million minutes x
1 billion minutes x
1 trillion minutes x
1 hour x
60 minutes
1 day =
24 hours
694 days
1 hour x
1 day x
1 year = 1.9 years
60 minutes 24 hours 365 days
1 hour x 1 day x 1 year = 1,903 years
60 minutes 24 hours 365 days
1 hour x 1 day x
1 year = 1,902,588 years
60 minutes 24 hours 365 days
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