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SCIENTIFIC NOTATION

Learn how to write numbers in scientific notation using the power of ten, mantissa, and exponent. Practice problems included. Also covers multiplication, division, addition, and subtraction in scientific notation.

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SCIENTIFIC NOTATION

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  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 DIGITto 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 103+2= 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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