Lesson 13
Multiplying, Dividing, and Estimating with Scientific Notation
Problem 1
Evaluate each expression. Use scientific notation to express your answer.
- \((1.5 \times 10^2) (5 \times 10^{10})\)
- \(\dfrac{4.8 \times 10^{\text-8}}{3 \times 10^{\text-3}}\)
- \((5 \times 10^8) (4 \times 10^3)\)
- \((7.2 \times 10^3) \div (1.2 \times 10^5)\)
Solution
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Problem 2
How many bucketloads would it take to bucket out the world’s oceans? Write your answer in scientific notation.
Some useful information:
- The world’s oceans hold roughly \(1.4 \times 10^{9}\) cubic kilometers of water.
- A typical bucket holds roughly 20,000 cubic centimeters of water.
- There are \(10^{15}\) cubic centimeters in a cubic kilometer.
Solution
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Problem 3
The graph represents the closing price per share of stock for a company each day for 28 days.
- What variable is represented on the horizontal axis?
- In the first week,
was the stock price generally increasing
or decreasing? - During which period did the closing price of the stock decrease for at least 3 days in a row?
![Line graph, horizontal, 0 to 28 by 2, vertical, 0 to 80 by 10. Segments roughly connect 1 comma 45 to 7 comma 62, to 10 comma 32, to 15 comma 58, to 17 comma 51, to 20 comma 70 to 28 comma 56.](https://staging-cms-im.s3.amazonaws.com/1QKTxUDxEU8LLUDUxYP1XjQf?response-content-disposition=inline%3B%20filename%3D%228-8.5.B5.PP.Image.102.png%22%3B%20filename%2A%3DUTF-8%27%278-8.5.B5.PP.Image.102.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240703%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240703T094120Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=644ef4a47aad877ae5a1045edff2f8df2bb299a6909ec354bf89c3ee47fb41b0)
Solution
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(From Unit 6, Lesson 5.)Problem 4
Write an equation for the line that passes through \((\text- 8.5, 11)\) and \((5, \text- 2.5)\).
Solution
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(From Unit 5, Lesson 9.)Problem 5
The point \((\text-3, 6)\) is on a line with a slope of 4.
- Find two more points on the line.
- Write an equation for the line.
Solution
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(From Unit 5, Lesson 10.)Problem 6
Explain why triangle \(ABC\) is similar to triangle \(CFE\).
![Coordinate plane, x 0 to 4, y 0 to 6. Line through point A, the origin, C at 1 comma 2, E at 3 comma 6. Segments connect A, & C to point B at 1 comma 0. Segments connect E & C to point F at 3 comma 2.](https://staging-cms-im.s3.amazonaws.com/5wXB9BTeAqmgr9KTQ3aLsAFM?response-content-disposition=inline%3B%20filename%3D%228-8.2.B.PP.Image.03.png%22%3B%20filename%2A%3DUTF-8%27%278-8.2.B.PP.Image.03.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240703%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240703T094120Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=991f90c7ca0fdc16a466e8ec1799af037a93738938276c5092d6c14efa373466)
Solution
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(From Unit 2, Lesson 11.)Problem 7
Two students join a puzzle solving club and get faster at finishing the puzzles as they get more practice. Student A improves their times faster than Student B.
![Coordinate plane, x, number of days of practice, 0 to 11 by ones, y, minutes to complete a puzzle, 0 to 7 by ones. Line l through 0 comma 6, and 7 comma 4. Line m through 0 comma 5, and 7 comma 4.](https://staging-cms-im.s3.amazonaws.com/1qYZaJK29kjGo2CCNcCFWHQc?response-content-disposition=inline%3B%20filename%3D%228-8.5.C8.PP.Image.105.png%22%3B%20filename%2A%3DUTF-8%27%278-8.5.C8.PP.Image.105.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240703%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240703T094121Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=cdb38598a22bbec1c90fa311d32da5fd032b6bfe9f46c501b74dfcbbad95ddb5)
- Match the students to the Lines \(\ell\) and \(m\).
- Which student was faster at puzzle solving before practice?
Solution
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(From Unit 6, Lesson 8.)