4-4 Scientific Notation
Warm Up
Problem of the Day
Lesson Presentation
Course 3
4-4 Scientific Notation
Warm Up
Order each set of numbers from least to
greatest.
1. 10 4, 10 –2, 100 , 10 –1
10–2, 10–1, 100, 104
2. 82, 8–2, 83 , 80
8–2, 80, 82, 83
3. 23 , 2–6 , 2–4, 21
2–6, 2–4, 21 , 23
4. 5.22, 5.29 , 5.2–1 , 5.2–2
5.2–2, 5.2–1, 5.22, 5.29
Course 3
4-4 Scientific Notation
Problem of the Day
Explain which problems you can or cannot solve.
1) 24 x 26
2) 43 x 812
3) n9 x m1
4) t7 x t13
Can solve 1 and
4 because the
bases are the
same
Course 3
Cannot solve 2
and 3 because
the bases are
not the same
4-4 Scientific Notation
Learn to express large and small
numbers in scientific notation and to
compare two numbers written in scientific
notation.
Course 3
4-4 Scientific Notation
Vocabulary
scientific notation:
• is a shorthand way of writing large or
small numbers by using a power of 10
• has to be a number
between 1 and 10
•Example: 1.7 or 9.4
Course 3
4-4 Scientific Notation
Examples of number written in standard
notation, that are easier to work with if
written in scientific notation.
An ordinary quarter contains about
97,700,000,000,000,000,000,000 atoms.
The average size of an atom is about
0.00000003 centimeters across.
The length of these numbers in standard
notation makes them awkward to work with.
Course 3
4-4 Scientific Notation
To express any number in scientific notation:
In standard notation the number of atoms in a
quarter is 97,700,000,000,000,000,000,000
In scientific notation the number of atoms in a
quarter is 9.77 1022
Course 3
4-4 Scientific Notation
Hint when expressing any number in
scientific notation:
A positive exponent means move the
decimal to the right
A negative exponent means move the
decimal to the left.
Course 3
4-4 Scientific Notation
Translating Scientific Notation to Standard Notation
Write the number in standard notation.
1.35
105
1.35
10
1.35
100,000
5
135,000
105 = 100,000
Think: Move the decimal
right 5 places.
Helpful Hint
A positive exponent means move the decimal to
the right, and a negative exponent means move
the decimal to the left.
Course 3
4-4 Scientific Notation
Translating Scientific Notation to Standard Notation
Write the number in standard notation.
2.01
104
20,100
Course 3
Think: Move the decimal
right 4 places.
4-4 Scientific Notation
Translating Scientific Notation to Standard Notation
Write the number in standard notation.
2.7
2.7
2.7
2.7
10–3
10–3
1
1000
1000
0.0027
Course 3
10
–3
1
=
1000
Divide by the reciprocal.
Think: Move the decimal
left 3 places.
4-4 Scientific Notation
Write the number in standard notation.
2.87
109
2,870,000,000
Course 3
Think: Move the decimal
right 9 places.
4-4 Scientific Notation
Write the number in standard notation.
1.9
10–5
0.000019
Course 3
Think: Move the decimal
left 5 places.
4-4 Scientific Notation
Write the number in standard notation.
5.09
108
509,000,000
Course 3
Think: Move the decimal
right 8 places.
4-4 Scientific Notation
Helpful Hint
A number less than 1 will have a negative
exponent when written in scientific notation.
Course 3
4-4 Scientific Notation
Translating Standard Notation to Scientific Notation
Write 0.00709 in scientific notation.
0.00709
7.09
7.09
10
Think: The decimal needs to move 3
places to get a number between 1 and
10.
Set up scientific notation.
Think: The decimal needs to move left to change 7.09
to 0.00709, so the exponent will be negative.
So 0.00709 written in scientific notation is 7.09
Check 7.09
Course 3
10–3 = 7.09
0.001 = 0.00709
10–3.
4-4 Scientific Notation
Write 0.000811 in scientific notation.
0.000811
8.11
Think: The decimal needs to move
4 places to get a number between
1 and 10.
8.11 10
Set up scientific notation.
Think: The decimal needs to move left to change
8.11 to 0.000811, so the exponent will be
negative.
So 0.000811 written in scientific notation is 8.11
Check 8.11
Course 3
10–4 = 8.11
10–4.
0.0001 = 0.000811
4-4 Scientific Notation
Life Science Application
A certain cell has a diameter of approximately
4.11 x 10-5 meters. A second cell has a diameter
of 1.5 x 10-5 meters. Which cell has a greater
diameter?
4.11 x 10-5
1.5 x 10-5
10-5 = 10-5
Compare powers of 10.
4.11 > 1.5
Compare the values
between 1 and 10.
4.11 x 10-5 > 1.5 x 10-5
The first cell has a greater diameter.
Course 3
4-4 Scientific Notation
A certain cell has a diameter of approximately
5 x 10-3 meters. A second cell has a diameter
of 5.11 x 10-3 meters. Which cell has a greater
diameter?
5 x 10-3
5.11 x 10-3
10-3 = 10-3
Compare powers of 10.
5 < 5.11
Compare the values
between 1 and 10.
5 x 10-3 < 5.11 x 10-3
The second cell has a greater diameter.
Course 3
4-4 Scientific Notation
Lesson Quiz: Part I
Write each number in standard notation.
1. 1.72
2. 6.9
104
17,200
10–3
0.0069
Write each number in scientific notation.
3. 0.0053
5.3
10–3
4. 57,000,000
5.7
107
5. Order the numbers from least to greatest.
T 2 10–4, 9 10–5, 7 10–5
7
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10–5, 9
10–5, 2
10–4
4-4 Scientific Notation
Lesson Quiz: Part II
6. A human body contains about 5.6 106
microliters of blood. Write this number in
standard notation. 5,600,000
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Textbook pgs. 177 #’s 21, 23, 25, 27, 29,
37, 39, 40, 41, 43, 45, 46, 49, 57, 58