Lesson 13

Multiplying, Dividing, and Estimating with Scientific Notation

Let’s multiply and divide with scientific notation to answer questions about animals, careers, and planets.

Problem 1

Evaluate each expression. Use scientific notation to express your answer.

  1. \((1.5 \times 10^2) (5 \times 10^{10})\)
  2. \(\dfrac{4.8 \times 10^{\text-8}}{3 \times 10^{\text-3}}\)
  3. \((5 \times 10^8) (4 \times 10^3)\)
  4. \((7.2 \times 10^3) \div (1.2 \times 10^5)\)

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.

Problem 3

The graph represents the closing price per share of stock for a company each day for 28 days.

  1. What variable is represented on the horizontal axis?
  2. In the first week,
    was the stock price generally increasing
    or decreasing?
  3. 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.
(From Unit 6, Lesson 5.)

Problem 4

Write an equation for the line that passes through \((\text- 8.5, 11)\) and \((5, \text- 2.5)\).

(From Unit 5, Lesson 9.)

Problem 5

The point \((\text-3, 6)\) is on a line with a slope of 4.

  1. Find two more points on the line.
  2. Write an equation for the line.
(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.
(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.
  1. Match the students to the Lines \(\ell\) and \(m\).
  2. Which student was faster at puzzle solving before practice?
(From Unit 6, Lesson 8.)