Exponents and Scientific Notation

Lesson 13

Math

Unit 1

8th Grade

Lesson 13 of 15

Objective


Multiply and divide with numbers in scientific notation. Interpret scientific notation on calculators.

Common Core Standards


Core Standards

  • 8.EE.A.4 — Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.

Criteria for Success


  1. Multiply two numbers in scientific notation by rearranging the factors as $${(a\times10^m)(b\times10^n) = (a\times b)(10^m\times10^n)}$$ using the commutative property.
  2. Divide two numbers in scientific notation by rearranging the factors as $$\left ( a\times10^m \right )\div\left ( b\times10^n \right )=\left ( \frac{a}{b} \right )\times\left ( \frac{10^m}{10^n} \right )$$.
  3. Apply the product and quotient properties of exponents to efficiently calculate with powers of 10.
  4. Use a calculator to multiply and divide in scientific notation and interpret the results (MP.5).

Tips for Teachers


Lesson Materials

  • Scientific calculator (1 per student) — These can be handheld or online.
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Anchor Problems


Problem 1

One sheet of $${8 {1\over2}}$$  " by $${11}$$ " paper weighs $${4.5\times10^{-3}}$$ kg. A school is expecting a delivery of $${100}$$ cases of paper which include a total of $${5\times10^5}$$ pieces of paper. How much does all the paper in the cases weigh? 

Guiding Questions

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Problem 2

Light travels at a speed of approximately $${300,000,000}$$ meters per second. If the sun is approximately $${1.5\times10^{11}}$$ meters from Earth, how long, in seconds, does it take for sunlight to reach Earth? How long is this in minutes?

Guiding Questions

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Problem 3

A student multiplied two numbers in an online scientific calculator and got the following result:

What does the answer in the calculator mean? 

What are possible factors that the student entered into the calculator?

Guiding Questions

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Problem 4

Calculate. Write your answer in scientific notation and standard form.

$${{6.6\times10^7\over{1.1\times10^{-1}}}\cdot {3\times10^{-5}}}$$

Guiding Questions

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Problem Set

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Target Task


Grizzly bears hibernate for up to 220 days per year. While they hibernate, Grizzly bears don’t eat. During the rest of the year, Grizzly bears eat up to $$5.8 × 10^4$$ calories per day.
What is the total number of calories a Grizzly bear eats in a year? Write your answer in decimal notation, scientific notation, and in words.

Student Response

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Additional Practice


The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

  • Include problems where a number written in scientific notation is taken to a power; for example, $${(3.2\times10^{-3})^5}$$.
  • Have students check their answers using scientific calculators.
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Lesson 12

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Lesson 14

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Review of Exponents

Topic B: Properties of Exponents

Topic C: Scientific Notation

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