Labeling Assignments
Title
Heading
Notes: 4.5 Scientific Notation
Last, First
Date
Period
4.5 Scientific Notation
Standards
8 EE: Expressions and Equations
3: Use numbers expressed in the form of a
single digit times an integer power of 10 to
estimate very large or very small quantities,
and to express how many as much one is than
the other.
Introduction
Evaluate the following powers:
1) 23
2)26
3) 20
4) 2−3
Evaluate and Simplify :
5) 103
6)106
7) 100
8) 10−3
9) Can you describe a shortcut for evaluating
the powers of 10 in problems 5-8 above?
Introduction KEY
Evaluate the following powers:
1)
23
8
2)26
64 3)
20
1
4)
𝟏
−3
2
𝟖
Evaluate and Simplify :
5) 103
6)106
7) 100
8) 10−3
1,000
.001 or
1,000,000
1
𝟏
𝟏,𝟎𝟎𝟎
9) Can you describe a shortcut for evaluating
the powers of 10 in problems 5-8 above?
**
Example 1: Evaluating Powers of 10
Find the value of each power of 10.
A. 10–6
B. 104
Start with 1 and
move the decimal
point six places to
the left.
Start with 1 and
move the decimal
point four places
to the right.
0.000001
10,000
C. 109
Start with 1 and
move the
decimal point
nine places to
the right.
1,000,000,000
Example 2: Writing Powers of 10
Write each number as a power of 10.
A. 1,000,000
B. 0.0001
The decimal point is
six places to the
right of 1, so the
exponent is 6.
The decimal point
is four places to
the left of 1, so
the exponent is –
4.
C. 1000
The decimal
point is three
places to the
right of 1, so
the exponent is
3.
Scientific Notation Video
O http://www.youtube.com/watch?v=H578qU
eoBC0
O http://www.youtube.com/watch?v=AWof6kn
vQwE
**
Scientific notation is a method of writing numbers that are
very large or very small. A number written in scientific notation
has two parts that are multiplied.
The 1ST part is a number between 1 and 10.
The 2ND part is a power of 10.
Example 3: Astronomy Application
Saturn has a diameter of about
Its distance from the Sun is about
1,427,000,000 km.
km.
Write Saturn’s diameter in standard form.
120000
120,000 km
Move the decimal point 5 places
to the right.
Example 5: Biology
According to wikipedia.com, a house dust
mite measures about 4.0 x 10-4 meters in
length.
Write the dust mite’s length in standard form.
4.0 x 10-4
4.0
0.0004
Move the decimal
point 4 places to
the left.
Example 4: Finance
According to forbes.com, Bill Gates, the
founder of Microsoft, is worth $6.7 x 1010.
Write Bill Gate’s worth in standard form.
6.7 x 1010
67,000,000,000 Move the decimal
point 10 places
$67,000,000,000
to the right.
Example 6: Finance
According to brillig.com, the current
national debt is currently about
$17,000,000,000,000.
Write the national debt in scientific notation.
17,000,000,000,000
17,000,000,000,000
Move the decimal point 13
places to the left.
13 places
1.7 x 1013
Example 7: Biology
The mass of a hydrogen atom is
0.0000000000000000000000016733 g.
Write the mass of a hydrogen atom in
scientific notation.
0.0000000000000000000000016733
24 places
1.6733  10-24 g
Move the decimal
point 24
places to the
right.
Example 8: Astronomy Application
Saturn has a diameter of about
km. Its
distance from the Sun is about 1,427,000,000 km.
Write Saturn’s distance from the Sun in scientific
notation.
1,427,000,000
1,4 2 7,0 0 0,0 0 0
Count the number of places
you need to move the
decimal point to get a
number between 1 and
10.
9 places
1.427 
109
km
Use that number as
the exponent of
10.
Questions
Classwork: 4.5A
Find the value of each expression.
1.
2.
3. The Pacific Ocean has an area of about
6.4 х 107 square miles. Its volume is about
170,000,000 cubic miles.
a. Write the area of the Pacific Ocean in
standard form.
b. Write the volume of the Pacific Ocean in
scientific notation.
CW 4.5B: Group Presentation
1.
Do some research on the Internet or library to find
interesting very small or very large numbers that occur in
the real world.
2.
Choose 1 very small and 1 very large number to discuss in
class.
3.
Create a presentation on Google:
•
1 Slide with Title
•
2 Slides with numbers in standard notation and
scientific notation
•
At least 1 imageand an explanation on what the
number represents.
•
4.
1 Slide with the references
Share your final product with the teacher.