Exponents and Scientific Notation

Lesson 12

Math

Unit 1

8th Grade

Lesson 12 of 15

Objective


Compare numbers written in scientific notation.

Common Core Standards


Core Standards

  • 8.EE.A.3 — Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 × 108 and the population of the world as 7 × 109, and determine that the world population is more than 20 times larger.
  • 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.

Foundational Standards

  • 4.NBT.A.1
  • 5.NBT.A.1
  • 5.NBT.A.2

Criteria for Success


  1. Compare two numbers, written in either standard form or scientific notation, to determine which one is larger or smaller. 
  2. Determine the number of times greater one quantity is than another quantity.
  3. Apply the properties of exponents to efficiently compare powers of 10. 
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Anchor Problems


Problem 1

The Fornax Dwarf galaxy is $${4.6\times10^5}$$ light-years away from Earth, while Andromeda is $${2.430\times10^6}$$ light-years away from Earth. Which is closer to Earth?

Guiding Questions

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References

EngageNY Mathematics Grade 8 Mathematics > Module 1 > Topic B > Lesson 13Exercise 1

Grade 8 Mathematics > Module 1 > Topic B > Lesson 13 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Problem 2

Subatomic particles are smaller than atoms. The average lifetime of the tau lepton particle is
$${2.906\times10^{-13}}$$ seconds, and the average lifetime of the neutral pion particle is $${8.4\times10^{-17}}$$ seconds. Which subatomic particle has a longer average lifetime?

Guiding Questions

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References

EngageNY Mathematics Grade 8 Mathematics > Module 1 > Topic B > Lesson 13Exercise 2

Grade 8 Mathematics > Module 1 > Topic B > Lesson 13 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Problem 3

The population of Fresno, CA is approximately 500,000 people. The population of California state is approximately $${4\times10^7}$$. How many times greater is the population of the state than the population of the city?

Guiding Questions

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Problem 4

A single piece of cat food weighs $${4.5\times10^{-4}}$$ kg. The plastic bowl that holds the cat food weighs 
$${9\times10^{-1}}$$ kg. The weight of the bowl is about how many times larger than the weight of a single piece of cat food?

Guiding Questions

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Problem Set

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Target Task


Nyan Cat travels at $$4.2\times10^2$$ miles per hour. Grumpy Cat travels at a pokey $$7\times10^{-1}$$ miles per hour.

a.   How many times faster is Nyan Cat traveling than Grumpy Cat?

b.   The Peregrine Falcon, the fastest bird, can fly up to half of Nyan Cat’s speed. How fast can a Peregrine Falcon fly? Write your answer in decimal notation and scientific notation.

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 students compare numbers written in scientific notation and standard form using inequality symbols $${<}$$ and $${>}$$.
  • Include error analysis problems where numbers were incorrectly compared by looking at only one component of numbers written in scientific notation (for example, $$3.5\times10^4 {>} 1\times10^5$$).
  • Include problems where students order numbers that are given in both scientific notation and standard form.
  • Challenge: How much larger is the mass of the sun than the mass of the earth?
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Lesson 11

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Lesson 13

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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