SCIENTIFIC NOTATION

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SCIENTIFIC NOTATION

• FOR WRITING VERY BIG AND VERY SMALL NUMBERS

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• Easy to recognize because they are written as a
  power of ten
• M X 108

EXPONENT large - small
MANTISSA ONLY SIG FIGS.
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TO WRITE A NUMBER IN SCIENTIFIC NOTATION

• Find the sig. figs.
• Move decimal between the 1st and 2nd sig. fig. ?
  MANTISSA
• of spaces and direction moved ? EXPONENT for
  the power of ten.
• left positive right negative

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• PROPER scientific notation form can only have ONE
  DIGIT to the LEFT of the decimal

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PRACTICE PROBLEMS

• WRITE IN PROPER SCI. NOTATION FORM
• 1) 405 000 000 000 mm
• 2) 0.000 000 000 670 cg

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ANSWERS

• 1) 4.05 X 1011mm
• 2) 6.70 X 10-10cg

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MATH WITH SCI. NOTATION (and SIG FIGS)

• MULTIPLICATION
• MULTIPLY MANTISSAS
• ADD EXPONENTS.
• Ex. (2.5 X 103 )(6.4 X 102)
• WORK (2.5 6.4) X 1032 16 X 105 must
  correct for improper form
• FINAL ANSWER 1.6 X 106

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Part of the work

• 2.5
• X 6.4
• 100
• 150
• 16.00

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• DIVISION
• DIVIDE MANTISSAS
• SUBTRACT BOTTOM EXPONENT FROM TOP
• Ex. 4.5 X 1012 / 3 X 10-2
• WORK (4.5 / 3) X 1012 (-2)
• 1.5 x 1014
• FINAL ANSWER 2 x 1014

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Part of the work
1.5

• 3
• 3
• 1 5
• 1 5
• 0

4.5
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• ADDITION
• MUST HAVE SAME EXPONENT. ACHIEVED BY MOVING
  DECIMAL PT. IN THE MANTISSA
• ADD MANTISSAS AND CARRY OVER EXPONENT.

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• Ex. (1.5 X 103) (3 X 102) ?
• WILL NOT MATTER WHICH EXPONENT YOU CHANGE
  WILL CHANGE 2 TO A 3
• MOVE DECIMAL ONE PLACE TO LEFT (positive move)
  NOW NUMBER BECOMES .3 X 103
• WORK(1.5 X 103) (.3 X 103) 1.8 X 103
• FINAL ANSWER 1.8 X 103

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Part of the work

• 1.5
• 0.3
• 1.8 X 103

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• SUBTRACTION
• MUST HAVE SAME EXPONENT. ACHIEVED BY MOVING
  DECIMAL PT. IN THE MANTISSA
• SUBTRACT MANTISSAS AND CARRY OVER EXPONENT.

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• Ex. (2.1 X 10-3) (5 X 10-2) ?
• WILL CHANGE 3 TO A 2
• MOVE DECIMAL TO LEFT ONE SPACE (positive move)
  NOW NUMBER BECOMES .21 X 10-2
• WORK(.21 X 10-2) (5 X 10-2)
• -4.79
  X 10-2
• FINAL ANSWER -5 X 10-2

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Part of the work

• 0.21 -5
• 5 OR 0.21
• -4.79 X 10-2

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PRACTICE PROBLEMS

• COPY AND WORK. ANSWERS MUST
• BE IN SCI. NOTATION WITH CORRECT
• SIG FIGS.
• (6.78 x 1028) (3.345 x 1027) ?
• (4.3 x 10-12) (7.89 x 10-11) ?
• (2.75 x 1025)(3.3 x 10-34) ?
• 4) (7.20 x 108) / (1.2 x 10-12)?

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ANSWERS

• 7.11 x 1028
• -7.46 x 10-11
• 9.1 x 10-9
• 4) 6.0 x 1020