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Mastering Scientific Notation with Negative Exponents

Learn to convert between scientific notation with negative exponents and standard form, practice with examples, and understand the difference between positive and negative exponents. Wrap it up with a summary!

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Mastering Scientific Notation with Negative Exponents

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Presentation Transcript

  1. Today’s lesson . . . What: Scientific Notation with Negative exponents Why? . . . so I can convert between numbers written in scientific notation (w/ negative exponents) and numbers written in standard form. How? . . . by engaging in lesson, completing notes, asking questions, and completing IXL homework with a smart score of 70% or more.

  2. How do you write a DECIMAL number in scientific notation (provide example) ?

  3. What is the difference between positive and negative exponents (when used in scientific notation)?

  4. What do you remember from last class ? small LARGE multiplication ten (10) power Example: 2.5 x 10-5 What about negative exponents ?? This is today’s focus!!

  5. To convert From scientific notation to a “regular #” . . . There are TWO STEPS: Locate the exponent– which tells you how many places to move decimal. Move decimal to the LEFT (exponent is the # of jumps), and add zeros in front as needed. For example: 2.95 x 10 -5 = ____________ Follow the above two steps. Since there is one digit to the left of the decimal already, we will need to add FOUR EXTRA ZEROS IN FRONT of the number– this makes 5 jumps total! Answer: 0.0000295 As soon as you see a NEGATIVE EXPONENT, think DECIMAL # !! We need 3 zeros in FRONT! 0.000009 0.00028 We need 6 zeros in FRONT! 0.0000702 0.000000405

  6. How do you write a decimal number in scientific notation ? As soon as you see a DECIMAL number, think NEGATIVE EXPONENT!!!! There are TWO STEPS: Locate the decimal. Move decimal until you make a number greater than 1, but less than 10 (# of “jumps” is the exponent number, but remember to add a negative sign)! For example: 0.00032 = ____________ Follow the above two steps. We need to “jump” the decimal point FOUR PLACES to the right in order to make a decimal greater than 1, but less than 10! Answer: 3.2 x 10 -4 3.4 x 10-5 1.02 x 10-4 5 jumps! 4.05 x 10-3 7 x 10-6 6 jumps!

  7. Mixed practice: 36,000 2.5 x 108 90,040,000 7.5 x 10-7 2.09 x 10-3 0.0000059 0.0072 5.723 x 109 As soon as you see a DECIMAL number, think NEGATIVE EXPONENT!!!!

  8. Wrap-it-up (summary): Provide an example of a number written in scientific notation (with a negative exponent) and give the answer. Explain the difference between scientific notation with positive exponents and scientific notation with negative exponents.

  9. END OF LESSON

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