Lesson 13Definition of Scientific Notation
Learning Goal
Let’s use scientific notation to describe large and small numbers.
Learning Targets
I can tell whether or not a number is written in scientific notation.
Lesson Terms
- scientific notation
Warm Up: Number Talk: Multiplying by Powers of 10
Problem 1
Find the value of each expression mentally.
Activity 1: The “Science” of Scientific Notation
Problem 1
The table shows the speed of light or electricity through different materials. Circle the speeds that are written in scientific notation. Write the others using scientific notation.
material | speed (meters per second) |
---|---|
space | |
water | |
copper (electricity) | |
diamond | |
ice | |
olive oil |
Activity 2: Scientific Notation Matching
Problem 1
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.
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Shuffle the cards and lay them facedown.
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Players take turns trying to match cards with the same value.
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On your turn, choose two cards to turn faceup for everyone to see. Then:
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If the two cards have the same value and 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.
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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.
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If the two cards do not have the same value, then set them facedown in the same position and end your turn.
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If it is not your turn:
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If the two cards have the same value and 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.
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Make sure both of you agree the cards have the same value.
If you disagree, work to reach an agreement.
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Whoever has the most points at the end wins.
Are you ready for more?
Problem 1
What is
A decimal
A fraction
Problem 2
What is
A decimal
A fraction
Problem 3
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
Problem 4
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
Problem 5
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?
Lesson Summary
The total value of all the quarters made in 2014 is 400 million dollars. There are many ways to express this using powers of 10. We could write this as
400 million dollars would be written as
Some other examples of scientific notation are
Thinking back to how we plotted these large (or small) numbers on a number line, scientific notation tells us which powers of 10 to place on the left and right of the number line. For example, if we want to plot