Comparison of Numbers Written in Scientific Notation

Examples, videos, and solutions to help Grade 8 students learn how to compare numbers expressed in scientific notation.

New York State Common Core Math Module 1, Grade 8, Lesson 13

Worksheets for Grade 8

Lesson 13 Student Outcomes

• Students compare numbers expressed in scientific notation.
• Students apply the laws of exponents to interpret data and use technology to compute with very large numbers.

Lesson 13 Summary

• Students have completed the lessons on exponential notation, the properties of integer exponents, magnitude, and scientific notation.
  
• Students can read, write, and operate with numbers expressed in scientific notation, which is the language of many sciences. Additionally, they can interpret data using technology.

Classwork

Example 1
Among the galaxies closest to Earth, M82 is about 1.15 x 10⁷ light-years away and Leo I Dwarf is about 8.2 x 10⁵ light-years away. Which is closer?

Exercise 1
The Fornax Dwarf galaxy is 4.6 x 10⁵ light-years away from Earth, while Andromeda I is 2.430 x 10⁶ light-years away from Earth. Which is closer to Earth?

Exercise 2
The average lifetime of the tau lepton 2.906 x 10^-13 is seconds and the average lifetime of the neutral pion is 8.4 x 10^-17 seconds. Explain which subatomic particle has a longer average lifetime.

Exploratory Challenge 1/Exercise 3
Theorem: Given two numbers in scientific notation, a x 10^m and b x 10ⁿ, if m < n, then a x 10^m < b x 10ⁿ

Example 3
Compare 1.815 x 10¹⁴ and 1.82 x 10¹⁴

Exercise 4
Compare 9.3 x 10²⁸ and 9.2879 x 10²⁸

Exercise 5
Chris said 5.3 x 10⁴¹ < 5.301 x 10²⁸ that because 5.3 has fewer digits than 5.301. Show that even though his answer is correct, his reasoning is flawed. Show him an example to illustrate that his reasoning would result in an incorrect answer. Explain.

Exploratory Challenge 2/Exercise 6
You have been asked to determine the exact number of Google searches that are made each year. The only information you are provided is that there are 35,939,938,877 searches performed each week. Assuming the exact same number of searches is performed each week for the 52 weeks in a year, how many total searches will have been performed in one year? Your calculator does not display enough digits to get the exact answer. Therefore, you must break down the problem into smaller parts. Remember, you cannot approximate an answer because you need to find an exact answer. Use the screen shots below to help you reach your answer.
Yahoo is another popular search engine. Yahoo receives requests for 1,792,671,335 searches each month. Assuming the same number of searches is performed each month, how many searches are performed on Yahoo each year? Use the screen shots below to help determine the answer.

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