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7-4: Scientific Notation

7-4: Scientific Notation. Essential Skills: Express numbers in scientific notation Find products & quotients of numbers in scientific notation. 7-4: Scientific Notation. Converting Standard Form → Scientific Notation

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7-4: Scientific Notation

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  1. 7-4: Scientific Notation Essential Skills:Express numbers in scientific notation Find products & quotients of numbers in scientific notation

  2. 7-4: Scientific Notation • Converting Standard Form → Scientific Notation • Step 1: Move the decimal point (left or right) until it is to the right of the first non-zero digit • Step 2: Note the number of places you moved and direction from step one • Step 3: • If the direction was to the left, the exponent is positive • If the direction was to the right, the exponent is negative • Write your answer as “a x 10n”, where n is your exponent • Step 4: Remove the unnecessary zeros

  3. 7-4: Scientific Notation • Example 1A: Standard → Scientific • Express 4,062,000,000,000 in scientific notation • 4,062,000,000,000 • Moved 12 spaces to the left • 4,062,000,000,000 = 4.062000000000 x 1012 • 4.062 x 1012

  4. 7-4: Scientific Notation • Example 1B: Standard → Scientific • Express 0.000000823 in scientific notation • 0.000000823 • Moved 7 spaces to the right • 0.000000823 = 8.23 x 10-7 • 8.23 x 10-7

  5. 1) Express 458,000,000 in scientific notation • 4.58 x 106 • 4.58 x 107 • 4.58 x 108 • 4.58 x 10-8

  6. 2) Express 0.0000452 in scientific notation • 4.52 x 104 • 4.52 x 10-4 • 4.52 x 105 • 4.52 x 10-5

  7. 7-4: Scientific Notation • Converting Scientific Notation → Standard Form • Step 1: Note whether the exponent n is positive or negative • Step 2 • If positive, move the decimal place to the right n spaces • If negative, move the decimal place to the left n spaces • Step 3: Insert the decimal point, zeros and commas as needed

  8. 7-4: Scientific Notation • Example 2A: Scientific → Standard • Express 6.45 x 105 in standard form • Exponent means we move 5 spaces to the right • 6.45 • 6.45 x 105 = 645000 • 645,000 000

  9. 7-4: Scientific Notation • Example 2B: Scientific → Standard • Express 1.8 x 10-3 in standard form • Exponent means we move 3 spaces to the left • 1.8 • 1.8 x 10-3 = 0.0018 • 0.0018 000

  10. 3) Express 3.16 x 10-2 in standard notation • 0.0316 • 0.00316 • 3.1600 • 316

  11. 4) Express 7.61 x 103 in standard notation • 0.00761 • 0.000761 • 761 • 7,610

  12. Participant Scores

  13. 7-4: Scientific Notation • Assignment • Page 417 - 418 • 1 – 9 & 21 – 35 • Odd problems only

  14. 7-4: Scientific Notation Day 2

  15. 7-4: Scientific Notation • Multiplying/Dividing numbers in scientific notation • Step 1: Multiply/Divide the non-exponent parts together • Step 2: Multiply/Divide the exponent parts together (meaning add/subtract the exponents) • Step 3: Readjust the non-exponent parts • If the value is > 10, shift the decimal point one space to the left and add one to the 10x exponent • If the value is < 1, shift the decimal point one space to the right and subtract one from the 10x exponent

  16. 7-4: Scientific Notation • Example 3: Evaluate (5 x 10-6)(2.3 x 1012) • (5)(2.3) = 11.5 • (10-6)(1012) = 106 • 11.5 x 106 • 1.15 x 107 • Example 4: Evaluate • 4.5 ÷ 1.5 = 3 • 108 ÷ 1010 = 10-2 • 3 x 10-2

  17. 5) Evaluate (8 x 105)(2.1 x 10-3) • 16.8 • 1.68 x 101 • 1.68 x 102 • 1.68 x 103

  18. 6) Evaluate • 4 x 103 • 4 x 10-3 • 4 x 10-2 • 4 x 10-1

  19. 7-4: Scientific Notation • Last year Afyu’s state registered over 400 thousand watercraft. Boat sales in her state generated more than $15.4 million in state sales taxes the same year. • Example 5A: Express the number of watercraft registered and sales tax generated from boat sales last year in standard notation. • 400 thousand = 400,000 • 15.4 million = 15,400,000

  20. 7-4: Scientific Notation • Last year Afyu’s state registered over 400 thousand watercraft. Boat sales in her state generated more than $15.4 million in state sales taxes the same year. • Example 5B: Write each number in scientific notation • 400,000 = 4 x 105 • 15,400,000 = 1.54 x 107

  21. 7-4: Scientific Notation • Last year Afyu’s state registered over 400 thousand watercraft. Boat sales in her state generated more than $15.4 million in state sales taxes the same year. • Example 5C: How many watercraft have been registered if 12 times the number last year have been registered in all? • (12)(4 x 105) = 48 x 105 • = 4.8 x 106

  22. 7) A local newspaper has a circulation of 150 thousand newspapers and receives about $1.2 million in advertising revenue. Express each in standard notation. • 1500$120,000 • 15,000$120,000 • 150,000$1,002,000 • 150,000$1,200,000

  23. 8) A local newspaper has a circulation of 150 thousand newspapers and receives about $1.2 million in advertising revenue. Express each in scientific notation. • 1.5 x 1031.2 x 105 • 1.5 x 1041.2 x 105 • 1.5 x 1051.2 x 106 • 1.5 x 1051.2 x 107

  24. 9) A local newspaper has a circulation of 150 thousand newspapers and receives about $1.2 million in advertising revenue. The newspaper predicts its advertising revenue will decrease by ½ next year as more people get their news from the internet. What will the advertising revenue be after this decrease? • 6 x 105 • 6 x 104 • 6 x 103 • 6 x 102

  25. Participant Scores

  26. 7-4: Scientific Notation • Assignment • Page 418 • 37 – 49, odds

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