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4-5 Scientific Notation
Activating Prior Knowledge - Notes
Order each set of numbers from least to greatest.
Evaluating Algebraic Expressions
1. 10 , 10 , 10 , 10
10–2, 10–1, 100 , 104
4
–2
0
3. 2 , 2 , 2 , 2
2–6, 21 , 23 , 24
3
–6
4
1
–1
2
3
2. 8 , 8 , 8 , 80
–2
8–2, 80, 82, 83
2
–2
–1
9
4. 5.2 , 5.2 , 5.2 , 5.2
–2
2
9
5.2 , 5.2 , 5.2 , 5.2
–1
Tie to LO
4-5 Scientific Notation
Learning Objective
Evaluating Algebraic Expressions
Today, we will express
large and small
numbers in scientific
notation.
CFU
4-5 Scientific Notation
Concept Development – Notes #1
Evaluating Algebraic Expressions
Scientific notation – A way to express
numbers that are very large or very
small.
CFU
4-5 Scientific Notation
Concept Development
– Notes #2
Evaluating Algebraic Expressions
The table shows relationships between several powers of
10.
• Each time you multiply by 10, the exponent in the
power increases by 1 and the decimal point in the
value moves one place to the right.
CFU
4-5 Scientific Notation
Concept Development
– Cont. Notes #2
Evaluating
Algebraic
The table
shows relationships
betweenExpressions
several powers of
10.
• Each time you divide by 10, the exponent in the
power decreases by 1 and the decimal point in the
value moves one place to the left.
CFU
4-5 Scientific Notation
Concept Development
– In Module
A positive,
finite decimal
s is said
to be
Evaluating
Algebraic
Expressions
written in scientific notation if it is expressed
as a product 𝒅 × 𝟏𝟎𝒏 , where 𝒅 is a finite
decimal so that 𝟏 ≤ 𝒅 < 𝟏𝟎, and n is an
integer.
The integer n is called the order of
magnitude of the decimal
𝒅 × 𝟏𝟎𝒏
CFU
4-5 Scientific Notation
Concept Development
The Evaluating
finite decimal
234.567Expressions
is equal to
Algebraic
every one of the following:
2.34567 x 102
0.234567 x 10
234.567 x 10
23.4567 x 10
234567 x 10
234567000 x 10−6
0
3
−3
Which is the only example of
scientific notation?
CFU
4-5 Scientific Notation
Concept Development
– Notes #4
Evaluating Algebraic Expressions
4.You can find the product of a number
and a power of 10 by moving the
decimal point of the number.
600
6 x 102
CFU
4-5 Scientific Notation
Concept Development
– Notes #5
Evaluating Algebraic Expressions
5. You may need to write zeros to the
right or left of the number in order to
move the decimal point.
.009
9x
−3
10
CFU
4-5 Scientific Notation
Concept Development
– Notes #6
Evaluating Algebraic Expressions
Multiply.
A. 1.4  104
1.40 0 0
14,000
CFU
4-5 Scientific Notation
Concept Development
Cont. Notes #6
–
Evaluating Algebraic Expressions
Multiply.
B. 2.3  10-4
0 0 0 2.3
0.00023
CFU
4-5 Scientific Notation
Skill Development/Guided Practice – Notes #7 & 8
Evaluating
Multiply.
7.
𝟒
𝟏. 𝟓 ∙ 𝟏𝟎
1.50000
15,000
Algebraic Expressions
Since the
exponent is
a positive 4,
move the
decimal
point 4
places to
the right.
8.
𝟏. 𝟐 ∙ 𝟏𝟎𝟓
1.20000
120,000
CFU
4-5 Scientific Notation
Skill Development/Guided Practice – Notes #9 & 10
Evaluating
Multiply.
9.
𝟐. 𝟎𝟖 ∙ 𝟏𝟎𝟓
2.080000
208,000
Algebraic Expressions
Since the
exponent is 10. 𝟏. 𝟏𝟑 ∙ 𝟏𝟎𝟖
a positive 3,
move the
1.130000000
decimal
point 3
113,000,000
places to
the right.
CFU
4-5 Scientific Notation
Concept Development
– Notes
#18
Evaluating
Algebraic
Expressions
Write the number in scientific notation.
A. 0.00709
Think: The decimal needs to move
3 places to get a number between 1
and 10.
7.09  10-3
Think: The number is less than 1, so
the exponent will be negative.
So 0.00709 written in scientific notation is 7.09  10–3.
CFU
4-5 Scientific Notation
Concept Development
– Cont. Notes #18
Evaluating Algebraic Expressions
Write the number in scientific notation.
B. 23,000,000,000
2.3  1010
Think: The decimal needs to
move 10 places to get a
number between 1 and 10.
Think: The number is greater
than 1, so the exponent will
be positive.
So 23,000,000,000 written in scientific notation is
2.3  1010.
CFU
4-5 Scientific Notation
Concept Development – Module Pg. S32
Evaluating
Algebraic
State
if the following
are in Expressions
scientific
notation? If not, state the reason.
1. 1.908  1017
2. 0.325 
10-2
3. 7.99 10³²
4. 4.0701 + 107
5. 18.432  58
6. 8  10-11
CFU
4-5 Scientific Notation
Concept Development
– Pair Share
Comparing Numbers in Scientific Notation
Evaluating
Expressions
A certain
cell has aAlgebraic
diameter of approximately
4.11  10-5 meters. A second cell has a diameter
of 1.5  10-5 meters. Which cell has a greater
diameter?
4.11  10-5
1.5  10-5
Compare the exponents.
4.11 > 1.5
Compare the values between
1 and 10.
Notice that 4.11  10-5 > 1.5  10-5.
The first cell has a greater diameter.
CFU
4-5 Scientific Notation
Concept Development
– Pair Share
A star has a diameter of approximately
Evaluating
Algebraic Expressions
3
5.11  10 kilometers. A second star has a
diameter of 5  104 kilometers. Which star has
a greater diameter?
5.11  103
5  104
Compare the exponents.
Notice that 3 < 4. So 5.11  103 < 5  104
The second star has a greater diameter.
CFU
4-5 Scientific Notation
Closure - Notes
1. What
did we learn
today? Expressions
Evaluating
Algebraic
2. Why is this important to you?
3. How do I write a number in scientific
notation?
Write in scientific notation.
5. 0.00034
4. 570,000
CFU
4-5 Scientific Notation
Exit Ticket
Write each number in standard form.
Evaluating Algebraic Expressions
1. 1.72  104 17,200
2. 6.9  10–3
0.0069
Write each number in scientific notation.
4. 57,000,000 5.7  107
3. 0.0053 5.3  10–3
5. Order the numbers from least to greatest.
T 2  10–4, 9  10–5, 7  10–5
7  10–5, 9  10–5, 2  10–4
6. A human body contains about 5.6  106
microliters of blood. Write this number in
standard notation. 5,600,000
CFU