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Section 1.7 Scientific Notation

Section 1.7 Scientific Notation. Powers of 10 Review Converting Numbers to Scientific Notation Converting Numbers from Scientific Notation Simplifying Computations. Powers of 10 - Review. Change to standard notation: 10 2 = 100 10 3 = 1000 10 6 = 1,000,000

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Section 1.7 Scientific Notation

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  1. Section 1.7 Scientific Notation • Powers of 10 Review • Converting Numbers to Scientific Notation • Converting Numbers from Scientific Notation • Simplifying Computations 1.7

  2. Powers of 10 - Review • Change to standard notation: • 102 = 100 • 103 = 1000 • 106 = 1,000,000 • 10n = 100,000 What is n? n = 5 • 10-1 = 0.1 • 10-2 = 0.01 • 10-7 = 0.0000001 • 10m = 0.00001 What is m? m = -5 • 103• 106 = 103+6 = 109 • 103÷ 107 = 103-7 = 10-4 • 104• 10-4 = 104+(-4) = 100 = 1 important! 1.7

  3. Scientific Notation For correct Scientific Notation, a single non-0 digit must precede the decimal point. 1.7

  4. Examples – Move the Decimal Point 4 positions – small number  5.17 ×10-4 8 positions – big number  5.23 ×108 1.7

  5. Examples – Converting & Computing 689300000000 Add 8 zeros (total 11 places)689,300,000,000 Put in commas from right = 1.12 • 5 • 10-8 • 10-7= 5.6x 10-15 1.7

  6. Adjusting to Correct Scientific Notation • Correct format is M ×10n where 1 ≤ M < 10 • Good Examples: 3.2 ×102 9.999 ×10-4 106 • WannaBe’s: • 432×103 Incorrect Format • 4.32×102×103 Convert 432 to Sci Not • 4.32 ×105Add the exponents • 0.00234×10-7 Incorrect Format • 2.34×10-3×10-7 Convert 0.00234 to Sci Not • 2.34 × 10-10Add the exponents 1.7

  7. Rounding Products & Quotients 1.7

  8. Simplifying Multiplication and Division Using Scientific Notation 4.0 × 10-3 2.1 × 102 2 × 1016 1.4 × 107 1.7

  9. What Next? • 2.1– Graphs 1.7

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