Lesson 12
Applications of Arithmetic with Powers of 10
Problem 1
Which is larger: the number of meters across the Milky Way, or the number of cells in all humans? Explain or show your reasoning.
Some useful information:
 The Milky Way is about 100,000 light years across.
 There are about 37 trillion cells in a human body.
 One light year is about \(10^{16}\) meters.
 The world population is about 7 billion.
Solution
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Problem 2
Write each number in scientific notation.
 14,700
 0.00083
 760,000,000
 0.038
 0.38
 3.8
 3,800,000,000,000
 0.0000000009
Solution
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Problem 3
Perform the following calculations. Express your answers in scientific notation.

\((2 \times 10^5) + (6 \times 10^5)\)

\((4.1 \times 10^7) \boldcdot 2\)

\((1.5 \times 10^{11}) \boldcdot 3\)

\((3 \times 10^3)^2\)
 \((9 \times 10^6) \boldcdot (3 \times 10^6)\)
Solution
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Problem 4
Jada is making a scale model of the solar system. The distance from Earth to the Moon is about \(2.389 \times 10^5\) miles. The distance from Earth to the Sun is about \(9.296 \times 10^7\) miles. She decides to put Earth on one corner of her dresser and the Moon on another corner, about a foot away. Where should she put the sun?
 On a windowsill in the same room?
 In her kitchen, which is down the hallway?
 A city block away?
Explain your reasoning.
Solution
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Problem 5
Diego was solving an equation, but when he checked his answer, he saw his solution was incorrect. He knows he made a mistake, but he can’t find it. Where is Diego’s mistake and what is the solution to the equation?
\(\displaystyle \begin{align} \text4(72x)=3(x+4)\\ \text288x=3x+12\\ \text28=11x+12\\ \text40=11x\\ \text{}\frac {40}{11}=x\ \end{align}\)
Solution
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(From Unit 4, Lesson 13.)Problem 6
Here is the graph for one equation in a system of equations.
 Write a second equation for the system so it has infinitely many solutions.
 Write a second equation whose graph goes through \((0,2)\) so that the system has no solutions.
 Write a second equation whose graph goes through \((2,2)\) so that the system has one solution at \((4,3)\).
Solution
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(From Unit 5, Lesson 13.)