Estimating with Scientific Notation

5 min

Teacher Prep
Setup
Display one problem at a time. 2 minutes of quiet think time, followed by a whole-class discussion.

Narrative

This activity introduces students to scientific notation that has been generated by technology. Technology may include physical and online calculators, apps, spreadsheet programs, and other digital tools that may display very large or very small numbers.

Launch

Give students 2 minutes of quiet think time followed by a whole-class discussion.

Student Task

Diego and Priya were calculating (5×1013)⋅(8×1025)(5\times10^{13})\boldcdot(8\times10^{25}). 

  • Diego used a calculator and his display read 4E394\text{E}39.
  • Priya used her knowledge of exponent rules and got 40×103840\times10^{38}.
  • Clare used an online calculator and the screen showed 4e+394e+39.

What do you think these different results mean?
 

Sample Response

Sample response: I think the “E” in Diego’s result and the “e” in Clare’s result both mean “×10\times10”. If we wrote Priya’s answer in scientific notation, it would be 4×10394\times10^{39}, so that means all 3 of them got the same result. 

Activity Synthesis (Teacher Notes)

The goal of this discussion is for students to understand the different ways scientific notation might be expressed by technology. Invite students to share their reasoning about Diego’s result. Here are some questions for discussion:

  • “How are Diego’s and Priya’s answers the same?” (They both have the same value.)
  • “How are Diego’s and Priya’s answers different?” (They have different factors. Diego’s result has a letter in it.)

If time allows, perform the calculation from the Task Statement on a calculator for all to see. Note that different calculators and programs may display scientific notation slightly differently. For example, some technology may use E, EE, or e.

Standards
Addressing
  • 8.EE.1·Know and apply the properties of integer exponents to generate equivalent numerical expressions. <em>For example, 3² × 3<sup>-5</sup> = 3<sup>-3</sup> = 1/3³ = 1/27.</em>
  • 8.EE.A.1·Know and apply the properties of integer exponents to generate equivalent numerical expressions. <span>For example, <span class="math">\(3^2\times3^{-5} = 3^{-3} = 1/3^3 = 1/27\)</span>.</span>
Building Toward
  • 8.EE.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.
  • 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.

25 min