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Understanding Scientific Notation in Chemistry: Managing Micro and Macro Scales

This lesson explores scientific notation, a crucial tool in chemistry for handling extremely large and small numbers. With examples such as the number of molecules in 1 ml of water and extensive practice on converting standard numbers into scientific notation, learners will grasp how to effectively utilize powers of ten for both micro and macro scales. Understanding positive and negative exponents is pivotal for representing numbers less than and greater than one. This lesson also features the "Powers of Ten" movie by Eames to visualize these concepts dynamically.

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Understanding Scientific Notation in Chemistry: Managing Micro and Macro Scales

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  1. Lesson 1-2 Scientific Notation

  2. Dealing with Micro and Macro • Scales in Chemistry • Eames Movie: Powers of Ten • Exponential (and Scientific) Notation • A mathematical system that keeps number easier to manage

  3. In Chemistry the Numbers are astronomically large! • Atoms are tiny, and to work with enough to measure we need huge numbers of them • 234,000,000,000 • 53,000,000,000,000,000,000 • 602,000,000,000,000,000,000,000 • Demonstration – number of molecules in 1 ml water • Chemists use a mathematical shortcut called “scientific notation” in order to keep the math manageable

  4. Scientific Notation • Scientific Notation is a shortcut that uses powers of 10 • Scientific Notation is when a whole number is multiplied by some factor of ten 90 = 9 x 101 900 = 9 x 102 9,000 = 9 x 103 90,000 = 9 x 104 900,000 = 9 x 105 4 x 103 = 4,000 5 x 105 = • All Numbers can be expressed this way using the format # x 10x

  5. Writing Numbers in Scientific Notation • Write 250 in scientific notation • What we want: a number in the form 2.5 x 10x • What we do: move decimal from the end until it gets next to the two250 . = 2.5 x 102

  6. More Practice • 450,000 = 4.5 x 10? • 345,678,000 = 3.45678 x 10? • 8765,000,000 =

  7. Positive and Negative Exponents • A positive exponent on the number ten means a number is greater than 1 300 = 3 x 102 3,000 = 3 x 103 30,000 = 3 x 104 • A negative exponent on the number ten means a number is less than 1 0.2 = 2 x 10-1 0.02 = 2 x 10-2 0.002 = 2 x 10-3

  8. Are the Exponents Positive or Negative? • When converting numbers to scientific notation we keep track of the direction and how many spaces we move a decimal… 0.00356 = 267,000 =

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