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Scientific Notation

Scientific Notation. Scientific Notation. Consists of two parts 1. mantissa The full size number that comes before x 10 2. characteristic The exponent that comes after x 10 and is superscript. Scientific Notation. Example: 3.00 x 10 15 Mantissa Characteristic. Scientific Notation.

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Scientific Notation

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  1. Scientific Notation

  2. Scientific Notation • Consists of two parts • 1. mantissa • The full size number that comes before x 10 • 2. characteristic • The exponent that comes after x 10 and is superscript

  3. Scientific Notation • Example: 3.00 x 1015 MantissaCharacteristic

  4. Scientific Notation • To convert a normal number to scientific notation, move the decimal either to the left or right until you have a mantissa which is greater than -10 or less than +10

  5. Scientific Notation • If the absolute value of the number is smaller than 1, the characteristic will be negative • If the absolute value of the number is larger than 1, the characteristic will be positive

  6. Scientific Notation • Example: 542 The absolute value of the number is greater than one so the characteristic is positive 542 Moved to the left two spaces 5.42 x 102

  7. Scientific Notation • Example: -45000000 The absolute value of the number is greater than one so the characteristic is positive -45000000 Moved to the left seven spaces -4.5 x 107

  8. Example: 0.0040 The absolute value of the number is less than one so the characteristic is negative 0.0040 Moved to the right three spaces 4.0 x 10-3

  9. Example: -0.209 The absolute value of the number is less than one so the characteristic is negative -0.209 Moved to the right one space -2.09 x 10-1

  10. Example: 9.245 The absolute value of the number is between -10 and +10. 9.245 The decimal is not moved. In this case, the characteristic is zero. 9.245 x100

  11. Expanding Scientific Notation to Regular notation • If the characteristic is positive, move the decimal to the right. • If the characteristic is negative, move the decimal to the left.

  12. Expanding Scientific Notation to Regular notation Example 6.50 x 102 The characteristic tells us to move two places to the right. 650.

  13. Expanding Scientific Notation to Regular notation Example 6.50 x 10-2 The characteristic tells us to move two places to the left. 0.0650

  14. Fixing Incorrect Scientific Notation • Fix the mantissa by moving the decimal • Add the “fixed” characteristic to the original characteristic

  15. Example 20.4 x 106 (incorrect) Moved over one space to the left (+) to correct the mantissa 2.04 x 10(6+1) 2.04 x 107 (correct)

  16. Example 200.4 x 10-6 (incorrect) Moved over two spaces to the left (+) to correct the mantissa 2.004 x 10(-6+2) 2.004 x 10-4 (correct)

  17. Example 0.00340 x 108 (incorrect) Moved over three spaces to the right (-) to correct the mantissa 3.40 x 10(8 + -3) 3.40 x 105 (correct)

  18. Example 0.00340 x 10-8 (incorrect) Moved over three spaces to the right (-) to correct the mantissa 3.40 x 10(-8 + -3) 3.40 x 10-11 (correct)

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