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Section 9.3

Section 9.3. What we are Learning: To express numbers in scientific and standard notation To find products and quotients of numbers expressed in scientific notation. Scientific Notation:. a x 10 n a ≥1 but < 10 NOT a decimal! n is an integer (…-2, -1, 1, 2…)

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Section 9.3

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  1. Section 9.3 What we are Learning: To express numbers in scientific and standard notation To find products and quotients of numbers expressed in scientific notation

  2. Scientific Notation: • a x 10n • a ≥1 but < 10 • NOT a decimal! • n is an integer (…-2, -1, 1, 2…) • We use Scientific Notation to express very large or very small numbers

  3. Scientific Notation for Large Numbers: • Express the number as a product of a number greater than or equal to 1 but less than 10, and a power of 10 • Place a decimal point after the first number • Count how many numbers, including zeros are after the decimal point • This is the number that will be your power of 10 • Example: 24,000,000,000 2.4000000000 2.4 x 1010

  4. Scientific Notation for Small Numbers: • Numbers between zero and one • The power of 10 will be negative • Place a second decimal point after the first non-zero number • Count the numbers between the two decimals • This will be your negative power of 10 • Example: .000065 .00006.5 6.5 x 10-5

  5. Examples: • 67,852,000 6.7852000 6.7852 x 107 • 0.000009345 0.000009.345 9.345 x 10-6

  6. Scientific Notation to Standard Notation: • For large numbers (positive powers of 10) • Count how many numbers come after the decimal • Subtract this amount from the power of 10 • This total is the number of zeros to add after the last number Example: 3.29 x 107 (There are two numbers after the decimal point) 7 - 2 = 5 (This is how many zeros to add after the last number) 32,900,000

  7. Scientific Notation to Standard Notation: • For small numbers (negative powers of 10) • Count how many numbers come before the decimal • Should ALWAYS be 1 • Add this number to the negative exponent • This is how many zeros to add before the first number • Example: 5.73 x 10-5 (there is one number before the decimal point) -5 + 1 = 4 (this is how many zeros to add before the first number) .0000573

  8. Examples: • 1.2475 x 1010 10 – 4 = 6 12,475,000,000 • Notice: • We can also solve the expression by 1.22475 x 10,000,000,000 12,475,000,000 • 4.7592 x 10-8 -8 + 1 = 7 .000000047592 • Notice: • We can also solve the expression by 4.7592 x (1/108) 4.7592 x (1/100,000,000) 4.7592/100,000,000 .000000047592

  9. Using Scientific Notation to Evaluate Expressions: • Write numbers in Scientific Notation • Use the Associative Property to group like terms together • Use the Properties of Powers

  10. Examples: • (392)(4,380,000) (3.92 x 102)(4.38 x 106) (3.92 x 4.38)(102 x 106) 17.1696 x 108 We need to have a number that is ≥ 1 and < 10. So we need to move the decimal one more place to the left… 1.71696 x 109 • (.00008562)(.00064) (8.562 x 10-5)(6.4 x 10-4) (8.562 x 6.4)(10-5 x 10-4) 54.7968 x 10-9 We need to have a number that is ≥ 1 and <10. So we need to move the decimal one more place to the left… 5.47968 x 10-8

  11. When We… • Move the decimal to the left to create 10<n≥1 we add to the exponent • Move the decimal to the right to create 10<n≥1 we subtract from the exponent

  12. Let’s Work These Together Write in Scientific Notation: Write in Standard Notation: 1.879 x 10-5 845 x 106 • 95,000,000 • 0.00000039

  13. Let’s Work These Together:Evaluate; Express in Scientific Notation and Standard Notation • (6.4 x 103)(7 x 104) • 3.372 x 10-6/4.8 x 10-2

  14. Homework: • Page 509, 510 • 19 to 39 odd

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