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CP Sci 9- 1st Sem.

Gen Chem - 1st Sem.

Working With Numbers



Dimensional Analysis:

Dimensional analysis is the name given to the process of converting units.

Example:  Convert the following to SI units.  75km/hr (Remember SI for length is the meter and SI for time is the second.)

       75km x 1000m x         h  = 75000m = 20.8333m/s or 2.1x101m/s (2 significant digits)

            h        km     x  3600s       3600s

The above problem was solved taking advantage of conversion factors or what is called unit equalities. (1km = 1000m)  Dimensional analysis is simply the method of organizing the unit equalities into an equation.  


    1)    Always place your given amount (75km/hr) first and orient it so that the units will cancel out.

    2)    Next place the unit equalities that you want to end up with on the right side of the problem.  In the case of the problem above I wanted to end up with m/s so I used the unit equalities 1000m = 1km and 1h = 3600s.  (Notice that I placed the meters and seconds in the appropriate orientation for my desired answer.)

    3)    Cancel out the units to make sure that you are ONLY left with the units that the answer requires.  (This is your check to make sure that you have set up the problem correctly.)

    4)    Solve the entire upper and lower portions of the equation.

    5)    Reduce the final amount and round to the appropriate significant digits.


Scientific Notation:

Scientific notation is a way that scientists make that incredibly large numbers used in science easier to work with.  There are 602,000,000,000,000,000,000,000 atoms in a mole of a substance.  It is much easier to use the answer as 6.02 x 1023.  


    1)    The answer must retain the correct amount of significant digits.

    2)    If the size of the number is to be reduced the exponent will be positive.  

(Rule: If the decimal is moved to the left, the exponent will be a positive number equal to the number of places the decimal was moved.)

Example:  398700 = 3.987 x 105  (the exponent is equal to the number of times that the decimal point was moved)

    3)    If the size of the number is to be increased the exponent will be negative.

(Rule: If the decimal is moved to the right, the exponent will be a negative number equal to the number of places the decimal was moved.)

Example:  0.00501 = 5.01 x 10-3


Percent Error & Percents:

Percent error calculations are used to compare test results to a known accepted quantity.  The formula is as follows:

Percent error = ((measured value - accepted value) / accepted value ) * 100%

Note:  The result can be positive or negative



Last modified: September 05, 2004