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

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602,000,000,000,000,000,000,000 6.02 X 10 23 ** Only 1 number to the left of the decimal

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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.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.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.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.

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Power of 10 1000 10 X 10 X 10 10 3 100 10 2 100 10 2 10 10 1 10 10 1 1 10 0 1 10 0 0.1 10 -1 0.1 10 -1 0.01 10 -2 0.01 10 -2 1/10 X 1/10 X 1X10 = 1/10 3 = 10 -3 Larger Smaller

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Learning Check 2500 = 2.5 X 10 3 0.25 X 10 2 = 2.5 X10 1 0.25 X 10 -2 = 2.5 X 10 -3

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

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

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Changing Numbers Into Scientific Notation500,0000.000,000,042285.20.0000283,700,000 5.0 X 10 5 4.2 X 10 -8 2.852 X 10 2 2 X 10 -4 8.37 X 10 7

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Changing Numbers Out Of Scientific Notation 4 X 10 -3 3.4 X 10 5 0.045 X 10 4 5.9 X 10 -6 0.004 340,000 450 0.0000059

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Adding and Subtracting ***Powers of 10 need to be the same. 3,200 3.2 X 10 3 3.2 X 10 3 + 250 2.5 X 10 2 +0.25 X 10 3 3,450 3.45 X 10 3 3.45X 10 3

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3.14 X 10 2 + 4.13 X 10 3 0.314 X 10 3 + 4.13 X 10 3 4.444 X 10 3

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6.3 X 10 3 - 2.3 X 10 2 6.3 X 10 3 - 0.23 X 10 3 6.07 X 10 3

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(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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