8.1.1.5
Grade 8 Unit 1 CCSSM1 Lesson 5 RIF
(Powers of 10 2)
Recommended time: 90 minutes
Domain:
Equations and Expressions
Cluster:
Work with radicals and integer exponents
Common Core Standard: 8.EE.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 times as much one is than the other.
Mathematical Practices: Make sense of problems and preserve in solving them
Model with mathematics
Attend to precision
Vocabulary: scientific notation – representation of a number as a multiplication expression where one
factor is greater than or equal to 1 but less than 10 and other factor is
a power of 10 in exponential form.
Essential Question: How can we represent very large numbers and small numbers using the number 10?
The Bridge:
Drake sold 3,000,000 song downloads in 2011. Your friend says that is the same as 3∙10∙10∙10∙10∙10∙10
song downloads. Is your friend correct? Explain. Is there another way to represent 3,000,000 using 3’s and
10’s (hint: think exponents).
Mini Lesson: 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 times as much one is than
the other. For example, estimate the population of the United States as 3 × 108 and the population
of the world as 7 × 109, and determine that the world population is more than 20 times larger.
Prove this to students by changing into standard notation and proving it is 20 times larger.
Show examples of comparing small 1 digit integers.
Examples: 8 vs. 2  8 is 4 times larger than 2.
3 vs. 9  9 is 3 times larger than 3.
From both of these examples (or more if needed), make sure students understand you are simply
dividing the larger number divided by the smaller number.
8.1.1.5
Show examples of comparing powers of 10.
Examples: 103 vs. 10  1,000 vs. 10  1000 is 100 times larger than 10  103 is 100 (102)
times larger than 10
10-4 vs. 10-8  .0001 vs. .00000001  .0001 is 10,000 times larger than .00000001 
10-4 is 10,000 (104) times larger than 10-8
From both of these examples (or more if needed), make sure students see the pattern of simply
subtracting the exponents rather than rewriting in standard notation and dividing.
Now put the last two ideas together:
Example: 8 x 103 vs. 2 x 10  since we are dividing to see how much larger one is versus the
other we can rewrite: (8 x 103) ÷ (2 x 10)
then rewrite vertically:
8 𝑥 103
2 𝑥 10
then separate into 2 fractions: =
then simplify:
=4x
8
2
𝑥
103
10
1000
10
= 4 x 100
= 400
So 8 x 103 is 400 times larger than 2 x 10
Give students time to see if they can develop a written explanation to determine it is 400 times
larger.
Possible explanation: 8 is 4 times larger than 2 and 103 is 100 times greater than 10 and 4 times
100 is 400, therefore 8 x 103 is 400 times larger than 2 x 10
Now show students an example where the first digits will divide to a number less than 1.
Example: 2 x 104 vs. 4 x 102
then rewrite vertically:
2 𝑥 104
4 𝑥 102
then separate into 2 fractions: =
2
4
𝑥
104
102
8.1.1.5
then simplify:
= .5 x
10,000
100
= .5 x 100
= 50
So 2 x 104 is 50 times larger than 4 x 102
Note: For this example, it would be beneficial to also show the that by performing the “shortcut”
method, a student would get 2 x 104 is .5 x 102 larger than 4 x 102. And .5 x 102 is 50 in standard
form.
Give more examples as needed, specifically examples that involve decimals (4.2 x 106 is 3000
times larger than 1.4 x 103) and those that involve negative exponents (8.6 x 10 -5 is 200 times
larger than 4.3 x 10-3).
Work Period: Watch the following video clip Western NY earthquake. Discuss with students about
earthquakes and how they are rated. Ask them if a 5.2 on the Richter Scale sounds a lot worse than a 4.2
earthquake, etc. Have students work on worksheet Earthquake Task to help them further understand the
Richter Scale and how powers of 10 are used to compare magnitudes of earthquakes.
Think and Discuss
1. Suppose your friend wasn’t in class today. Tonight on the phone, they ask what they
missed in math class today. What are the important points you would tell your friend?
How would you explain these important points?
Summary/Closure: Have students answer the essential question.
Journal Entry – Ask students to think about how exponents can be used to write large
and small numbers more efficiently. Have students write an explanation about why this
is useful and give examples to demonstrate the efficiency of this method.
Homework: Handout – This homework could be given out over 2 days (1 page per day) if this is a 45
minute class.
Learning Extensions: Think about where else extremely large numbers and extremely small numbers are
used (distances, measurements, money, etc.). Discuss why it would be helpful to represent these numbers
using powers of 10. Could this different notation also cause confusion? Explain.
8.1.1.5
Additional Resources: Exponents with base 10
8.1.1.5
Work Period – Earthquake Task
Name: _____________________________
Lesson #5
Powers of 10
Work Period
A number from 0 to 9 describes the strength of earthquakes on the Richter scale. The Richter
scale is an exponential scale, which uses powers of 10 to compare the magnitude or size of
earthquakes. Complete the chart below to get a sense of how the Richter scale works.
Type of
earthquake
Richter
scale
Multiplication
problem
Exponential
notation
No movement
0
1
10 0
Not felt
1
10
101

Not felt
10  10
2
10 2

10  10  10
Felt at
epicenter
3
Mild
4 
Moderate
5
Strong
6
Very Strong
7
Great
8


The difference in magnitude of earthquakes can be expressed as exponents with a base of 10.
For example: there are two earthquakes, one with a magnitude of 5 and the other 7; the
difference is 2. This means that one of these earthquakes is 10 2 , or 100 times as powerful as
the other.

8.1.1.5
On the table below are 10 of the most powerful earthquakes of the twentieth century. The
difference between 9.5 and 9.2 is 0.3. Using a calculator, we find that 10 0.3 =2. This means
that an earthquake registering 9.5 is twice as powerful as one that registers 9.2. Use your
calculator to answer the questions below.

Year
1960
1964
2004
2011
1952
2010
1906
1965
2005
1950
Ten Most Powerful Earthquakes
Location
Chili
Prince William Sound, Alaska
Off the Coast of Northern Sumatra
Near the East Coast of Honshu, Japan
Kamchatka, Russia
Offshore Maule, Chile
Off the Coast of Ecuador
Rat Islands, Alaska
Northern Sumatra, Indonesia
Assam - Tibet
Richter Scale
9.5
9.2
9.1
9.0
9.0
8.8
8.8
8.7
8.6
8.5
Source: earthquake.usgs.gov
1. How much more powerful is an earthquake that registers 9.5 than one that registers
8.5?
2. In 2011, a major 9.0 earthquake struck about 100 miles off the coast of Japan. This
happened only 1 year after 8.8 earthquake hit Chile. How much more powerful was
the earthquake in Japan than the one in Chile.
3.
In 2010, an earthquake in Haiti, registered 7.0 on the Richter scale. The death toll has
been estimated at about 316,000 people. Yet 15,538 people died because of the
earthquake (and resulting tsunami) in Honshu, Japan although it registered 9.0 on the
Richter scale. How much more powerful was the earthquake in Haiti compared to the
earthquake in Honshu?
4.
Why do you think there is greater loss of life in earthquakes with lower magnitudes
compared to other earthquakes with higher magnitudes?
8.1.1.5
Name: _____________________________
Lesson #5
Powers of 10
Homework
4
1) What is 10 as a fraction and as a decimal?
2) Express in exponent form: 0.001

3) Express as a decimal:
4)
10 5 
a.

1
10000

1
10 5
b. .00005
c. 10,000
d. 100,000


In problems #5-9 match the power of ten with the number. Write he letter for each answer on the line next to
the problem number.
_________5) 10 2
a) 0.01
_________6) 101

b) 100
10 0
_________7)

c)
10 2

_________8)
_________9) 10 1



1
10
d) 1
e) 10
8.1.1.5
Rewrite each number as power of 10.
10) 100,000 = ________
11) 100,000,000 = ________
13) Sue lost the 200 meter race by
12) 10,000 = ________
1
of a second.
100
Part A
Describe the time by which Sue lost the 200 meter race as an expression with a negative exponent.

Part B
Use what you know about exponents with a base 10 to explain why your answer is correct. Use words
and/or numbers to support your explanation.
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
14) The brittle star is a type of starfish. A certain species of brittle star has a skeleton that is covered in
microscopic crystals. Scientists have discovered that these crystals act as lenses that allow the brittle star to
sense light.
Part A
The surface of each crystal has an area of
1
square meters. Write this number using a negative
1,000,000,000
exponent.

Answer: _______ square meters
Part B
Approximately 9.98 x 1000 crystals cover the skeleton of a brittle star. Find the total number of crystals.
Answer:_______crystals
8.1.1.5