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Dimensional Analysis Scientific Notation

Learn how to apply scientific notation and dimensional analysis to solve problems in mathematics and science. Practice converting numbers to scientific notation and calculating with dimensional analysis.

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Dimensional Analysis Scientific Notation

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  1. Dimensional Analysis Scientific Notation

  2. Objectives: • Today I will be able to: • Apply scientific notation to problem solving. • Calculate multiplication and division problems using scientific notation. • Apply dimensional analysis to solving metric coversions • Informal Assessment – monitoring student interactions as they complete the scientific notation practice • Formal assessment – math assessment/scientific notation practice and exit ticket • Common Core Connection • Make sense of problem and persevere in solving them • Model with mathematics

  3. Lesson Sequence • Evaluate: Warm-Up • Explain: Scientific Notation Notes • Elaborate: Scientific Notation Practice • Explain: Dimensional Analysis Notes • Elaborate: Dimensional Analysis Practice • Evaluate: Exit Ticket

  4. Warm- Up • Place the following numbers into scientific notation • 0.00071m • 5200 g • 0.04 L • What is the purpose of putting numbers into scientific notation?

  5. Objective • Today I will be able to: • Apply scientific notation to problem solving. • Calculate multiplication and division problems using scientific notation. • Apply dimensional analysis to solving metric coversions

  6. Homework • Complete the dimensional analysis practice • Wear closed toed shoes for lab on Wednesday and Thursday

  7. Agenda • Warm-Up • Scientific Notation Notes • Scientific Notation Practice • Dimensional Analysis Notes • Dimensional Analysis Practice • Exit Ticket

  8. Scientific Notation Notes

  9. In groups, brainstorm 3 examples of things that scientists/ engineers could study that would be large enough or small enough for scientific notation to be used to describe them

  10. Standard Notation to Scientific Notation cont. • Examples • 489000000 (Standard Notation) • Move the decimal to the left, exponent is positive • 4.89 x 108 (Scientific Notation) • Numbers greater than 1 always have a positive exponent in scientific notation • 0.000123 (Standard Notation) • Move the decimal to the right, exponent is negative • 1.23 x 10-4 • Numbers less than 1 always have a negative exponent in scientific notation

  11. Scientific Notation to Standard Notation cont. • Examples • 3.47 x 105 (Scientific Notation) • Exponent is positive, move to the right • 347000 (Standard Notation) • 7.82 x 10-4 (Scientific Notation) • Exponent is negative, move to the left • 0.000782 (Standard Notation)

  12. Multiplying/Dividing in Scientific Notation • Multiply or divide the numbers first • (don’t include x 10exp) • When multiplying, add the exponents together • When dividing, subtract the exponents • Make sure there is only one number before the decimal place in scientific notation. You may have to move the decimal so there is only one

  13. Multiplying/Dividing Scientific Notation cont. • Examples • (2.0 x 105)(7.0 x104)= • 1.4 x 1010 • (15.0 x 107) / (3.0 x 109)= • 5.0 x 10-2

  14. Scientific Notation Practice Complete the practice at your desk. We will review selected answers as a class.

  15. Dimensional Analysis Notes

  16. Conversion Factor 12 inches 1 foot 7 days 1 week .5 ½ • A Fraction that is equal to the number one • Two quantities that equal the same thing

  17. Dimensional Analysis • Do these two fractions equal the same quantity? 1 dozen 12 eggs 12 eggs 1 dozen Yes!

  18. Dimensional Analysis Problem Solving Tips Read the problem Write down what you are given, put it over 1 Write down what you are looking for List all possible conversion factors for the problem Make a road map Solve the problem

  19. Practice Problem 1 10 hours 1 • How many minutes are there in 10 hours? • Read the problem • Write down what you are given, put it over 1 • Write down what you are looking for. • The number of minutes

  20. Practice Problem 1 Cont 1 hour60 minutes 60 minutes 1 hour • List all possible conversion factors for the problem • We know that one hour = 60 minutes • Make a road map • Hours ? Minutes

  21. Practice Problem 1 Cont. 10 hours . 1 hour = 10 hours 2 1 60 minutes 60 minutes • Solve the problem • We also know that when you multiply, if 2 quantities are placed in opposite corners of each other, they will cancel out • Incorrect, the units do not cancel out

  22. Practice Problem 1 cont. 10 hours . 60 minutes = 600 minutes 1 1 hour Solve for Correct Answer!

  23. Practice Problem 2 • How many minutes are there in 12 weeks? • 12,096 minutes Weeks  Days  Hours  ? Minutes 12 weeks . days . hours . minutes = week day hour . 12 weeks . 7 days . 24 hours . 60 minutes = 1 week 1 day 1 hour

  24. Practice Problem 3 • How many minutes are there in 2 years? • Years  Weeks  Days  Hours  Minutes 2 years . weeks . days . hours . minutes = 1 year week day hour 2 years . 52 weeks . 7 days . 24 hours . 60 minutes = 1 1 year 1 week 1 day 1 hour = 1,048,320 minutes or 1,051,200 minutes (365 days)

  25. Practice Problem 4 500 mL . 1 Liter = 0.500 L 1 1000 mL How many liters are in 500 mL? mL  ? L

  26. Practice Problem 5 20 kg . 1000 g . 1000 mg = 2 x 107 mg 1 1 kg 1 g How many milligrams are there in 20 kg? kg  g  ? mg

  27. Dimensional Analysis Practice

  28. Exit Ticket • Activity • Find your matching partner by finding the correct standard notation and scientific notation pair • With your partner discuss the following questions: • If you could have one special superhero power, what would it be? • Would you rather have Cheetos fingers, or a popcorn kernel stuck in the back of your throat, for the rest of your life?

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