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SCIENTIFIC NOTATION

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SCIENTIFIC NOTATION FOR WRITING VERY BIG AND VERY SMALL NUMBERS Easy to recognize because they are written as a power of ten M X 108 MANTISSA: ONLY SIG FIGS. – PowerPoint PPT presentation

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Title: SCIENTIFIC NOTATION


1
SCIENTIFIC NOTATION
  • FOR WRITING VERY BIG AND VERY SMALL NUMBERS

2
  • Easy to recognize because they are written as a
    power of ten
  • M X 108

EXPONENT large - small
MANTISSA ONLY SIG FIGS.
3
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

4
  • PROPER scientific notation form can only have ONE
    DIGIT to the LEFT of the decimal

5
PRACTICE PROBLEMS
  • WRITE IN PROPER SCI. NOTATION FORM
  • 1) 405 000 000 000 mm
  • 2) 0.000 000 000 670 cg

6
ANSWERS
  • 1) 4.05 X 1011mm
  • 2) 6.70 X 10-10cg

7
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

8
Part of the work
  • 2.5
  • X 6.4
  • 100
  • 150
  • 16.00

9
  • 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

10
Part of the work
1.5
  • 3
  • 3
  • 1 5
  • 1 5
  • 0

4.5
11
  • ADDITION
  • MUST HAVE SAME EXPONENT. ACHIEVED BY MOVING
    DECIMAL PT. IN THE MANTISSA
  • ADD MANTISSAS AND CARRY OVER EXPONENT.

12
  • 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

13
Part of the work
  • 1.5
  • 0.3
  • 1.8 X 103

14
  • SUBTRACTION
  • MUST HAVE SAME EXPONENT. ACHIEVED BY MOVING
    DECIMAL PT. IN THE MANTISSA
  • SUBTRACT MANTISSAS AND CARRY OVER EXPONENT.

15
  • 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

16
Part of the work
  • 0.21 -5
  • 5 OR 0.21
  • -4.79 X 10-2

17
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)?

18
ANSWERS
  • 7.11 x 1028
  • -7.46 x 10-11
  • 9.1 x 10-9
  • 4) 6.0 x 1020
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