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CP Sci 9- 1st Sem.

Gen Chem - 1st Sem.

Working With Numbers:

Objectives:

    1.    Define significant digits.

    2.    Explain how to determine which digits in measurement are significant.

    3.    Convert measurements in to scientific notation.

Key Terms:

    significant digit    percent error    density

Web Resources:

 

Notes:

Significant Digits:

The purpose of significant digits is to limit the amount of uncertainty in the data you display.  The measured and the estimated digits of a measurement are considered significant.  (example: If you look at the picture the significant digits would be read as 26.45g.  26.4 measured, .05 estimated)  

Rules:

    1)    Zeros that simply hold places are not significant.

        A)    No decimal point.

                Example: 1050 

                       

 

        B)    With a decimal point.

                Example: 0.001050 

               

    2)    If numbers are on both sides of the decimal point, all are significant.

            Example:  21.00356 

            

Significant Digits In Calculations:

Rules:

    1)    Exact numbers or conversion factors do not affect the significant digits of a calculation. (Example: 100 centimeters in a meter)

    2)    Multiplication & Division - the measurement with the smallest amount of significant digits determines the significant digits of the answer.

           Example:  120.0 * 0.0030 * 150.004 = 

               

 

    3)    Addition & Subtraction - the total cannot be more accurate than the least accurate measurement.  This time the amount of significant digits of each number does not matter.  The quantity with the least digits to the right of the decimal point determines the accuracy of the answer.

           Example:  420.1 + 3501 + 0.1123 + 1.2 = 

               

 

    4)    When doing combinations of the above, all digits are carried to the end.  The digits in the end answer are determined by the last operation performed.

 

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.  

Rules:

    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.

Example:  398700 = 3.987 x 10(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.

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 but the answer is always represented as the absolute value

 

 

Last modified: September 05, 2004