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4.8 Scientific Notation

4.8 Scientific Notation. Why use scientific notation??. When working with very large (astronomical!) numbers or very small (microscopic!) numbers, it is easier to write the numbers in scientific notation. . Ex.

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4.8 Scientific Notation

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  1. 4.8 Scientific Notation

  2. Why use scientific notation?? Whenworking with very large (astronomical!) numbers or very small (microscopic!) numbers, it is easier to write the numbers in scientific notation.  Ex. We can estimate the number of stars in the Milky Way galaxy as roughly 100 billion (100,000,000,000) The diameter of a hydrogen atom is 0.00000000024 m

  3. We can estimate the number of stars in the Milky Way galaxy as roughly 100 billion (100,000,000,000) The diameter of a hydrogen atom is 0.00000000024 m It is MUCH easier to write these numbers using scientific notation. There are two parts to scientific notation… The number (which MUST be greater than or equal to 1 and less than 10) 2. The number 10 with an exponent A positive exponent indicates a large number. A negative exponent indicates a small number.

  4. We can estimate the number of stars in the Milky Way galaxy as roughly 100 billion (100,000,000,000) To write 100,000,000,000 in scientific notation, “move the decimal point” so that the number part is between 1 and 10, count as you move… 100,000,000,000 11 10 9 8 7 6 5 4 3 2 1 In scientific notation…. 1.0 * 1011

  5. The diameter of a hydrogen atom is 0.00000000024 m To write 0.00000000024 in scientific notation, “move the decimal point” so that the number part is between 1 and 10, count as you move… 0.00000000024 1 2 3 4 5 6 7 8 9 10 In scientific notation…. 2.4 * 10-10

  6. Examples: STANDARD FORM SCIENTIFIC NOTATION 300 3.0  × 102 3000 3.0  × 103 3250 3.25  × 103 32,500,000 3.25  × 107 3.0  × 10-2 0.03 3.0  × 10-4 0.0003 3.25  × 10-8 0.0000000325 3.2  × 10-10 0.00000000032

  7. SCIENTIFIC NOTATION STANDARD FORM 3.0  × 102 300 3.0  × 103 3000 3.25  × 103 3250 10 raised to an exponent 3.25  × 107 32,500,000 3.0  × 10-2 0.03 3.0  × 10-4 0.0003 0.0000000325 3.25  × 10-8 0.00000000032 3.2  × 10-10 Number between 1 and 10 When writing a number in scientific notation there are 2 parts: The number (which MUST be greater than or equal to 1 and less than 10) 2. The number 10 with an exponent A positive exponent indicates a large number. A negative exponent indicates a small number.

  8. Now try some: EXERCISES:  Express in scientific notation. 1.     450 = ___________________ 2.     7500 = ___________________ 3.     12,000,000 =   ___________________ 4.     720,000,000,000 = ___________________ 5.     0.00325 = ___________________ 6.     0.000000246 = ___________________ 7.     0.00000000325 = _______________                  8.     0.00000000436 = _________________ 9.     480,000,000 = __________________               10.     93,200,000,000 = ________________

  9. Now try some: EXERCISES:  Express in standard notation. 1) 2 x 103 = ___________________ 2) 2.331 x 105 = ___________________ 3) 9.51 x 1012 = ___________________ 4) 5 x 10-3 = ___________________ 5) 7.6278 x 10-5 = ___________________ 6) 2.12 x 10-2 = ___________________ 7) 3.14 x 10-4 =___________________ 8) 5.213 x 103 =___________________ 9) 7.49 x 104 =___________________ 10) 9.2 x 102 =___________________

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