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Scientific Notation

Scientific Notation. What is Scientific Notation?. A way of expressing really big or really small numbers. Most often used in “scientific” calculations where the analysis must be very precise. Why use Scientific Notation?.

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Scientific Notation

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  1. Scientific Notation

  2. What is Scientific Notation? • A way of expressing really big or really small numbers. • Most often used in “scientific” calculations where the analysis must be very precise.

  3. Why use Scientific Notation? • Very large and very small numbers can be converted into scientific notation to express them in a more concise form. • Numbers expressed in scientific notation can be used in a computation with far greater ease.

  4. Scientific notation consists of two parts: • A number between 1 and 10 • A power of 10 • The exponent may be positive or negative. N x 10x

  5. Are they in scientific notation? • 23.98393 x 109 • 4.19385930 x 104 • 9820.1888 x 10-3 • 2.22221 x 10000 • 9.002 x 100 • 3.9992934 x 101 • 1.01 x 1056 • 2.39403 x 10-23 • 9.00078 x 10-1

  6. Changing standard form to scientific notation.

  7. To change standard form to scientific notation… Place the decimal point so that there is only one non-zero digit to the left of the decimal point. Ex: 2,250,000  2.250000 Count the number of decimal places the decimal point has “moved” from the original number. This will be the exponent on the 10. 2,250,000  2.250000  2.25 x 106

  8. Continued… If the original number was less than 1, then the exponent is negative. If the original number was greater than 1, then the exponent is positive. Ex: .0029 = 2.9 x 10-3

  9. Example 1 • Given: 289,800,000 • Use: 2.898 (moved 8 places) • Answer: 2.898 x 108

  10. Example 2 • Given: 0.000567 • Use: 5.67 (moved 4 places) • Answer: 5.67 x 10-4

  11. Changing scientific notation to standard form

  12. To change scientific notation to standard form… • Move the decimal point to the right for positive exponent 10. • Move the decimal point to the left for negative exponent 10. (Use zeros to fill in places.)

  13. Examples 3.9456 x 106 (Positive exponent goes right. It’s a big number!) 3,954,600 8.0965 x 10-4 (Negative exponent goes left. It’s a tiny number!) .00080965

  14. Example 3 Given: 5.093 x 106 Answer: 5,093,000 (moved 6 places to the right. Big Number)

  15. Example 4 Given: 1.976 x 10-4 Answer: 0.0001976 (moved 4 places to the left. Itty bitty number.)

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