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Understanding Scientific Notation Operations

Learn to multiply, divide, add, and subtract in scientific notation. Practice problems and step-by-step explanations included for better comprehension. Strengthen your math skills with this unit focusing on Common Core Standards.

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Understanding Scientific Notation Operations

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  1. Warm Up • Write down objective and homework in agenda • Lay out homework (Multiply & Divide wkst) • Homework (Operations worksheet)

  2. Unit 4 Scientific NotationCommon Core Standards • 8.EE.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 32 x 3-3= 3-3= 1/33 = 1/27. • 8.EE.3 Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. • 8.EE.4 Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. • 8.NS.1 Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. • MP.1 Make sense of problems and persevere in solving them. • MP.2 Reason abstractly and quantitatively. • MP.4 Model with mathematics. • MP.5 Use appropriate tools strategically. • MP.6 Attend to precision.

  3. Warm Up

  4. Warm Up-Answers • 5.32 x 1012 • 6.11 x 10 4 • 6 x 10-2 • 1.2 x 107

  5. Adding and Subtracting… • The important thing to remember about adding or subtracting is that the exponents must be the same! • If the exponents are not the same then it is necessary to change one of the numbers so that both numbers have the same exponential value.

  6. Adding… • The general format for adding is as follows… • (N x 10x) + (M x 10x) = (N + M) x 10x • The first step, if necessary, is to change one of the numbers so that both numbers have the same exponential value.

  7. Adding With the Same Exponent • (3.45 x 103) + (6.11 x 103) • 3.45 + 6.11 = 9.56 • 9.56 x 103

  8. Practice • Given: 2.56 X 103 + 6.964 X 103 • Add: 2.56 + 6.964 = 9.524 • Answer: 9.524 X 103

  9. Adding With Different Exponents • (4.12 x 106) + (3.94 x 104) • (412 x 104) + (3.94 x 104) • 412 + 3.94 = 415.94 • 415.94 x 104 • Express in proper form: 4.15 x 106

  10. Practice • Given: 2.46 X 106 + 3.476 X 103 • Shift decimal 3 places to the left for 103. • Move: .003476 X 103+3 • Add: 2.46 X 106 + .003476 X 106 • Answer: 2.463 X 106

  11. Subtracting… • The general form for subtracting is as follows… • (N x 10x) – (M x 10x) = (N – M) x 10x • The first step, if necessary is to change one of the numbers so that both numbers have the same exponential value. (Just like adding).

  12. Subtracting… • Secondly, subtract the M number from the N number and express as an answer. • The final step is to multiply the result by the 10x. • (It may be necessary to put the resulting answer into proper scientific notation.)

  13. Subtracting With the Same Exponent • (8.96 x 107) – (3.41 x 107) • 8.96 – 3.41 = 5.55 • 5.55 x 107

  14. Practice • Given: 9.49 X 105 – 4.863 X 105 • Subtract: 9.49 – 4.863 = 4.627 • Answer: 4.627 X 105

  15. Subtracting With Different Exponents • (4.23 x 103) – (9.56 x 102) • (42.3 x 102) – (9.56 x 102) • 42.3 – 9.56 = 32.74 • 32.74 x 102 • Express in proper form: 3.27 x 103

  16. Practice • Given: 5.762 X 103 – 2.65 X 10-1 • Shift decimal 4 places to the right for 10-1. • Move: .000265 X 10(-1+4) • Subtract: 5.762 X 103-.000265 X 103 • Answer: 5.762 X 103

  17. Practice! • http://www.mathworksheets4kids.com/scientific-notations/addition-subtraction-1.pdf

  18. You Try!

  19. Answers

  20. Practice • http://www.regentsprep.org/Regents/math/ALGEBRA/AO2/page5a.htm

  21. Links for more information and practice • Addition and Subtraction with Scientific Notation • Problem Solving--Scientific Notation • Scientific Notation

  22. Now it’s your turn. • Use the link below to practice adding numbers in scientific notation. • Adding Numbers in Scientific Notation

  23. Now it’s your turn. • Use the link below to practice subtracting numbers in scientific notation. • Subtracting Numbers in Scientific Notation

  24. Quiz Time!!! • Below is a set of links for a quiz on adding and subtracting numbers in scientific notation, and there is a link to get the answers to the quiz. • Adding and Subtracting Quiz • Answers to Quiz

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