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Scientific Notation?

Scientific Notation?. Scientific notation is a way of expressing really big numbers or really small numbers. Use only Significant Figures. 602,000,000,000,000,000,000,000 6.02 X 10 23 ** Only 1 number to the left of the decimal. COEFFICIENT. Power of ten.

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Scientific Notation?

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  1. Scientific Notation? • Scientific notation is a way of expressing really big numbers or really small numbers. • Use only Significant Figures.

  2. 602,000,000,000,000,000,000,000 6.02 X 1023 ** Only 1 number to the left of the decimal COEFFICIENT Power of ten

  3. To change standard form to scientific notation… • Place the decimal point so that there is one non-zero digit to the left of the decimal point. • Count the number of decimal places the decimal point has “moved” from the original number. This will be the exponent on the 10. • 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.

  4. Power of 10 1000  10 X 10 X 10  103 100  102 10  101 1  100 0.1  10-1 0.01  10-2 1/10 X 1/10 X 1X10 = 1/103 = 10-3 Larger Smaller

  5. Learning Check 2500 = 2.5 X 103 0.25 X 102 = 2.5 X101 0.25 X 10-2 = 2.5 X 10-3

  6. To change scientific notation to standard form… • Simply 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.)

  7. Example • Given: 5.093 x 106 • Answer: 5,093,000 (moved 6 places to the right) • Given: 1.976 x 10-4 • Answer: 0.0001976 (moved 4 places to the left)

  8. Changing Numbers Into Scientific Notation 5.0 X 105 4.2 X 10-8 2.852 X 102 2 X 10-4 8.37 X 107 500,000 0.000,000,042 285.2 0.00002 83,700,000

  9. Changing Numbers Out Of Scientific Notation 4 X 10-3 3.4 X 105 0.045 X 104 5.9 X 10-6 0.004 340,000 450 0.0000059

  10. Adding and Subtracting ***Powers of 10 need to be the same. 3,200  3.2 X 103  3.2 X 103 + 250 2.5 X 102  +0.25 X 103 3,450  3.45 X 103  3.45X 103

  11. 3.14 X 102 + 4.13 X 103 0.314 X 103 + 4.13 X 103 4.444 X 103

  12. 6.3 X 103 - 2.3 X 102 6.3 X 103 - 0.23 X 103 6.07 X 103

  13. (6.6 X 10-8) + (5.0 X 10-9) = 7.1 X 10-8 (6.7 X 10-2) – (3.0 X 10-3) = 6.4 X 10-2

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