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Scientific Notation. http://www.ieer.org/clssroom/scidrill.html. Why and What?. Scientific notation provides a place to hold the zeroes that come after a whole number or before a fraction.
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Scientific Notation http://www.ieer.org/clssroom/scidrill.html
Why and What? • Scientific notation provides a place to hold the zeroes that come after a whole number or before a fraction. • The number 100,000,000 for example, takes up a lot of room and takes time to write out, while 108 is much more efficient.
Why and What? What About 1 Mole: 602,300,000,000,000,000,000,000 OR 6.023 x1023
base exponent coefficient Why and What? 5.67 x 105 OR: 567,000
Basics • COEFFICIENT must be greater or equal to one and less than 10. • BASE – always 10 • EXPONENT – number of zeros before or after decimal in coefficient
100= 1 101= 10 102= 100 103= 1000 104= 10,000 105= 100,000 106= 1,000,000 107= 10,000,000 10-0= 1 10-1-.1 10-2= .01 10-3= .001 10-4= .0001 10-5= .00001 10-6= .000001 10-7= .0000001 Basics
Basics – Changing Form • Look at EXPONENT • Positive Exponent, move decimal exponent number of places to right. • Negative Exponent, move decimal exponent number of places to left 2.00 x 102 = 200. 2.00 X 10-2 = 0.0200
Basics – Changing Form • Decimal to SN format: • If you move decimal to right, exponent is negative • If you move decimal to left, exponent is positive 200. = 2.00 x 102 0.0200 = 2.00 X 10-2
Adding/Subtracting • Convert SN numbers to have SAME Exponent value • Add/Subtract Coefficients • Exponent stays the same • Reform sum/difference into correct SN by moving decimal and changing exponent
Multiplication Scientific notation provides a place to hold the zeroes that come after a whole number or before a fraction. The number 100,000,000 for example, takes up a lot of room and takes time to write out, while 108 is much more efficient. Model: (2 x 102) x (6 x 103) = 12 x 105 = 1.2 x 106
Multiplication • Multiply Coefficients • ADD exponents • Reform into correct SN by moving decimal and changing exponent
Division Section F: Division (a little harder - we basically solve the problem as we did above, using multiplication. But we need to "move" the bottom (denomenator) to the top of the fraction. We do this by writing the negative value of the exponent. Next divide the first part of each number. Finally, add the exponents). (12 x 103) Model: ----------- = 2 x (103 x 10-2) = 2 x 101 = 20 (6 x 102)
Division • Divide coefficients • SUBTRACT exponents • Reform into SN
