Definition of Scientific Notation: IM 8.7.13
[url=https://im.kendallhunt.com/MS/teachers/3/7/13/preparation.html]“Definition of Scientific Notation”[/url] from IM Grade 8 by [url=https://www.geogebra.org/m/gus8ffvr]Open Up Resources[/url] and Illustrative Mathematics. Licensed under the [url=https://creativecommons.org/licenses/by/4.0/]Creative Commons Attribution 4.0 license[/url].
Table of Contents
- Lesson 8.7.13
- IM 8.7.13 Lesson: Definition of Scientific Notation
- Practice 8.7.13
- IM 8.7.13 Practice: Definition of Scientific Notation
IM 8.7.13 Lesson: Definition of Scientific Notation
Find the value of each expression mentally.
[math]123\cdot10,000[/math]
[math](3.4)\cdot1,000[/math]
[math](0.6)\cdot100[/math]
[math](7.3)\cdot(0.01)[/math]
The table shows the speed of light or electricity through different materials. Circle the speeds that are written in scientific notation.
Your teacher will give you and your partner a set of cards. Some of the cards show numbers in scientific notation, and other cards show numbers that are not in scientific notation.[br][list=1][*]Shuffle the cards and lay them facedown.[br][/*][*]Players take turns trying to match cards with the same value.[br][/*][*]On your turn, choose two cards to turn faceup for everyone to see. Then:[br][list=1][*]If the two cards have the same value [i]and[/i] one of them is written in scientific notation, whoever says “Science!” first gets to keep the cards, and it becomes that player’s turn. If it’s already your turn when you call “Science!”, that means you get to go again. If you say “Science!” when the cards do not match or one is not in scientific notation, then your opponent gets a point.[br][/*][*]If both partners agree the two cards have the same value, then remove them from the board and keep them. You get a point for each card you keep.[br][/*][*]If the two cards do not have the same value, then set them facedown in the same position and end your turn.[br][/*][/list][/*][*]If it is not your turn:[br][list=1][*]If the two cards have the same value [i]and[/i] one of them is written in scientific notation, then whoever says “Science!” first gets to keep the cards, and it becomes that player’s turn. If you call “Science!” when the cards do not match or one is not in scientific notation, then your opponent gets a point.[br][/*][*]Make sure both of you agree the cards have the same value.[br]If you disagree, work to reach an agreement.[br][/*][/list][/*][*]Whoever has the most points at the end wins.[br][/*][/list]
[size=150][size=100]What is [math]9\times10^{-1}+9\times10^{-2}[/math]? Express your answer as: a decimal.[/size][/size]
What is [math]9\times10^{-1}+9\times10^{-2}[/math]? Express your answer as: a fraction.
[size=150][size=100]What is [math]9\times10^{-1}+9\times10^{-2}+9\times10^{-3}+9\times10^{-4}[/math]? Express your answer as: a decimal.[/size][/size]
What is [math]9\times10^{-1}+9\times10^{-2}+9\times10^{-3}+9\times10^{-4}[/math]? Express your answer as: a fraction.
The answers to the two previous questions should have been close to 1. What power of 10 would you have to go up to if you wanted your answer to be so close to 1 that it was only [math]\frac{1}{1,000,000}[/math] off?
What power of 10 would you have to go up to if you wanted your answer to be so close to 1 that it was only [math]\frac{1}{1,000,000,000}[/math] off? [br]Can you keep adding numbers in this pattern to get as close to 1 as you want? Explain or show your reasoning.
[size=100]Imagine a number line that goes from your current position (labeled 0) to the door of the room you are in (labeled 1). In order to get to the door, you will have to pass the points 0.9, 0.99, 0.999, etc. The Greek philosopher Zeno argued that you will never be able to go through the door, because you will first have to pass through an infinite number of points. What do you think? How would you reply to Zeno?[/size]
IM 8.7.13 Practice: Definition of Scientific Notation
Write each number in scientific notation.
Perform the following calculations. Express your answers in scientific notation.
Jada is making a scale model of the solar system.
The distance from Earth to the Moon is about [math]2.389\times10^5[/math] miles. The distance from Earth to the Sun is about [math]9.296\times10^7[/math] miles. She decides to put Earth on one corner of her dresser and the Moon on another corner, about a foot away. Where should she put the sun?[br][list][*]On a windowsill in the same room?[/*][*]In her kitchen, which is down the hallway?[/*][*]A city block away?[/*][/list]Explain your reasoning.
Here is the graph for one equation in a system of equations.
Write a second equation for the system so it has infinitely many solutions.
Write a second equation whose graph goes through [math](0,2)[/math] so that the system has no solutions.
Write a second equation whose graph goes through [math](2,2)[/math] so that the system has one solution at [math](4,3)[/math].