[math]123\cdot10,000[/math]
[math](3.4)\cdot1,000[/math]
[math](0.6)\cdot100[/math]
[math](7.3)\cdot(0.01)[/math]
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]