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8.5 Scientific Notation

8.5 Scientific Notation. Objectives: Recognize the need for special notation in scientific calculations. Perform computations involving scientific notation.

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8.5 Scientific Notation

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  1. 8.5 Scientific Notation Objectives: Recognize the need for special notation in scientific calculations. Perform computations involving scientific notation. Standards Addressed: 2.1.8.A: Represent and use numbers in equivalent forms. 2.1.8.B: Simplify numerical expressions involving scientific notation.

  2. A number written in scientific notation is a product with two factors: a number from 1 to 10, including 1 but not including 10, and a power of 10. • The first factor includes only significant digits (0s are included only if they lie between two other digits) and is often rounded to simplify the notation. • Therefore, all numbers written in scientific notation are considered approximations.

  3. Large number  POSITIVE EXPONENT • Decimal NEGATIVE EXPONENT

  4. Multiplying by Powers of 10 • If the exponent is positive, move the decimal point to the right. • If the exponent is negative, move the decimal point to the left.

  5. Follow these steps to write a number in scientific notation. Step 1: First, move the decimal point after the first nonzero digit. Step 2: Then, find the power of ten by counting the decimal places. Step 3: When the number is greater than one, the exponent of 10 is positive. Step 4: When the number is between zero and one, the exponent of 10 is negative.

  6. Ex. 1A

  7. Ex. 1B Write 875,000 in scientific notation. 8.75 X 105

  8. Ex. 2A

  9. Ex. 2B • Write 0.0000000402 in scientific notation. 4.02 x 10-8

  10. Ex. 3 Write Each # in decimal notation. • A. 3.67 X 104 • 36,7000 • B. 4.103 X 10-5 • .00004103 • C. 3.001 X 10-8 • .0000000301 • D. 4.3 x109 • 4,300,000,000

  11. Ex. 4 Express the product & quotient in Scientific Notation. • A. • B.

  12. Ex. 4 Express the product & quotient in Scientific Notation. • C. • (8 x 3) (104 x 103) • 24 X 107 • (2.4 x 101) X 107 • 2.4 x 108 • D. • 4 x 104

  13. Ex. 4 Express the product & quotient in Scientific Notation. • E. • (6 x 1015) ÷ 103 • 6 x 1012 • F. • (3 x 4) (103 X 10-5) • 12 x 10-2 • 1.2 x 101 x 10-2 • 1.2 x 10-1 (6 x 1015) ÷ 1000________________________ (3 x 103) (4 x 10-5) ____________________

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