IM 8 Ch 8.2.4 How Do I Compute It
CPM Materials modified by Mr. Deyo
What part of the expression is being raised to a power?
What are the factors?
How can we rewrite the expression to have fewer
terms?
Common Core Standard: 8.EE.4
IM 8 Ch 8.2.4 How Do I Compute It
By the end of the period, I will compute with numbers written in scientific notation and connect these computations to the work with simplifying exponent expressions.
I will demonstrate this by completing Four‑Square notes and by solving problems in a pair/group activity.
Learning TargetTitle: IM8 ‑ Ch. 8.2.4 How Do I Compute It? Date:
IM 8 Ch 8.2.4 How Do I Compute It
Home Work: Sec. 8.2.4Desc. Date Due
Review & Preview
4 Problems 8‑109, 8‑110, 8‑111, 8‑112
IM 8 Ch 8.2.4 How Do I Compute It
IM 8 Ch 8.2.4 How Do I Compute It
Vocabulary1) Base
2) Exponent
3) Scientific Notation
IM 8 Ch 8.2.4 How Do I Compute It
IM 8 Ch 8.2.4 How Do I Compute It
8.2.4 How Do I Compute It?Scientific notation is an application of exponents and the base 10 system. It is very useful when writing very large numbers, like the distance to Alpha Centauri, which is 4.13 × 1016 m, or the radius of the hydrogen atom, which is 5.29 × 10−11 m. But what if you wanted to know how many times larger the distance to Alpha Centauri is than the hydrogen atom? How would you calculate this? What if you wanted to add or subtract two numbers written in scientific notation? In this lesson, you will learn how to do operations with numbers written in scientific notation.
What part of the expression is being raised to a power?
What are the factors?
How do we properly write the expression in scientific
notation?
IM 8 Ch 8.2.4 How Do I Compute It
8100. A typical dwarf sperm whale, the planet’s smallest whale species, weighs about 3 × 102 pounds. A blue whale, the planet’s largest whale, might weigh about 4.5 × 105 pounds. Estimate about how many times heavier a blue whale is than a dwarf sperm whale, without using a calculator.
IM 8 Ch 8.2.4 How Do I Compute It
b) When the baker multiplied, her calculator displayed the answer. What do you think her calculator is
displaying? Explain.
8101. There are about 1.8 × 1021 molecules in one gram of table sugar (C12H22O11). A baker uses 8 × 102 grams in a recipe for cinnamon pastries.
a) How many molecules of sugar does the baker use? Do not use your calculator.
IM 8 Ch 8.2.4 How Do I Compute It
8102. Find (1.75 × 1020)(6.01 × 1014) in scientific notation without using a calculator.
Then check your answer with your calculator. Write down exactly what your calculator displayed.
IM 8 Ch 8.2.4 How Do I Compute It
8103. The average distance from the sun to the earth is 1.488 × 1011 meters. If the length of the average paperclip is 3 × 10−2 meters, how many paperclips would need to be connected together to reach the sun?
IM 8 Ch 8.2.4 How Do I Compute It
8104. Jeremiah wanted to do the following problem. However, he was not sure how to get started, because the numbers were in scientific notation. He knew that if he wrote them out in standard form, without scientific notation, then he could line up the numbers with the same place value and add them together. He does not want to have to do that, though, because he does not want to write all of those zeroes. He is worried that he might just get more confused if he did write them all out. Work with your team to find a way to add the numbers required without first rewriting them in standard form. Here is the problem Jeremiah wanted to solve:
The average distance of each of the first five planets from sun is shown in the table below. Is the distance to Jupiter more or less than the combined distances of the first four planets (Mercury, Venus, Earth, and Mars)?
The distance to Jupiter is ________ than the combined distances of the first four planets.
IM 8 Ch 8.2.4 How Do I Compute It
8105. The United States Department of Agriculture reported in Vegetables and Melons Outlook in 2007 that the average American consumes about 7.4 × 103 potato chips in a year. Since Idaho had about 1.5 × 106 people in 2007, how many potato chips would Idaho residents have consumed in 2007? Without using a calculator, make an exact computation and record your answer in scientific notation.
IM 8 Ch 8.2.4 How Do I Compute It
8106. One of the giant pyramids of Egypt is made of about 2.4 × 106 carved blocks of stone. If each block weighs approximately 4.95 × 103 pounds, about how many pounds of block make up the pyramid?
IM 8 Ch 8.2.4 How Do I Compute It
a)
c)
8107. Simplify.
1.24 × 103 + 2.3 × 104
b)
8.5 × 1010 · 7.6 × 1012
4 x 105
8 x 107
IM 8 Ch 8.2.4 How Do I Compute It
8108. Additional Challenge: The radius of the earth is about 6 × 108 cm.
mass volume
b) Density can be found from
The earth’s mass is about 6 × 1024 kg. Without a calculator, estimate the earth’s density. Answer in scientific notation.
a) The volume of a sphere can be estimated by
where r is the radius of the sphere.
8821V = r3
Without using a calculator, estimate the earth’s volume in scientific notation.
IM 8 Ch 8.2.4 How Do I Compute It
a)
c)
8109. Compute each product or quotient. Convert the final answer to scientific notation if necessary.
(3 × 102)(2 × 103)
b)
(2.75 × 10−2)(2.5 × 108)
8 x 1012
4 x 107
http://homework.cpm.org/cpmhomework/homework/category/CC/textbook/CC3/chapter/Ch8/lesson/8.2.4/problem/8109
IM 8 Ch 8.2.4 How Do I Compute It
a)
c)
8110. Use the laws of exponents to simplify the following expressions.
(x2)(x5) b)
*d)
y7
y4
63m5
65m6 x3 x4
http://homework.cpm.org/cpmhomework/homework/category/CC/textbook/CC3/chapter/Ch8/lesson/8.2.4/problem/8110
.
IM 8 Ch 8.2.4 How Do I Compute It
8111. For the following examples, tell whether there is positive association, negative association, or no association.
a) The number of inches of rain per hour and the height of water in a reservoir.
c) The height of a tree and the amount of nutrients it gets.
b) The amount of food a person eats and how many pets he or she has.
d) The number of hours spent hiking in the mountains and the amount of water left in your water bottle.
http://homework.cpm.org/cpmhomework/homework/category/CC/textbook/CC3/chapter/Ch8/lesson/8.2.4/problem/8111
IM 8 Ch 8.2.4 How Do I Compute It
8112. Silvia has a picture from her trip to the Grand Canyon. The photo is 4 inches tall by 6 inches wide.a) She would like to make a larger photo for her wall that is as big as possible. The widest the enlarged photo can be is 48 inches. How tall will the enlarged photo be?
b) Silvia also wants a walletsized photo to carry around and show her friends. She wants it 1.5 inches tall. How wide will it be?
http://homework.cpm.org/cpmhomework/homework/category/CC/textbook/CC3/chapter/Ch8/lesson/8.2.4/problem/8112
IM 8 Ch 8.2.4 How Do I Compute It
8113. Since the beginning of school, Steven has been saving money to buy a new MP3 player. His bank balance is represented by the graph.
a) According to the graph, about how much money had Steven saved after 2 weeks of school?
c) If he keeps saving at the same rate, how much will he have saved by Week 7? Explain how you know.
http://homework.cpm.org/cpmhomework/homework/category/CC/textbook/CC3/chapter/Ch8/lesson/8.2.4/problem/8113
b) About how much money did Steven probably have after 4 weeks of school?
How can you tell?
IM 8 Ch 8.2.4 How Do I Compute It
8114. The science club is selling homemade cookies to raise money for a field trip. The club members know that 12 dozen cookies uses 3 pounds of flour. Use that information to solve each part below.
a) How much flour is needed for 18 dozen cookies?
http://homework.cpm.org/cpmhomework/homework/category/CC/textbook/CC3/chapter/Ch8/lesson/8.2.4/problem/8114
b) How many cookies can be made with 10 pounds of flour?
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