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    Ramapo High School                                           Physics                                                                Dr. Lu 

    Topic: Scientific Method, Model, Theory and Scientific Notation with Significant Digit and Proper Unit

    1.Significant digit

    The term significant figures refers to the number of important single digits (0 through 9 inclusive) in the coefficient of an expression in scientific notation . The number of significant figures in an expression indicates the confidence or precision with which an engineer or scientist states a quantity.

    Rule

    1) ALL non-zero numbers (1,2,3,4,5,6,7,8,9) are ALWAYS significant.

    2) ALL zeroes between non-zero numbers are ALWAYS significant.

    3) ALL zeroes which are SIMULTANEOUSLY to the right of the decimal point AND at the end of the number are ALWAYS significant.

    4) ALL zeroes which are to the left of a written decimal point and are in a number >= 10 are ALWAYS significant.

     5) In a number without a decimal point, trailing zeros may or may not be significant. More information through additional graphical symbols or explicit information on errors is needed to clarify the significance of trailing zeros.

    6)  Leading zeros are never significant.

     

    Number

    # Significant

    Figures

    Rule(s)

    48,923

    5

    1

    3.967

    4

    1

    900.06

    5

    1,2,4

    0.0004 (= 4 E-4)

    1

    1,4,6

    8.1000

    5

    1,3

    501.040

    6

    1,2,3,4

    3,000,000 (= 3 E+6)

    1

    1, 5

    10.0 (= 1.00 E+1)

    3

    1,3,4
         

    2.Scientific Notation = a number (between 1 and 10) times 10 to a power , e.g.  3.4 x102

    3.Order of magnitude

      3.2x 102,  the order of magnitude is 102 since 3.2  is  < 5

                       We round it down to 1 and 3.2x102   ==> 102

       7.5x 10-2, the order of magnitude is 10 – 1.

       Explanation: since  7.5 > 5 , we round it up to 10 and  the 7.5x 10-2 will become 10x10 -2

                                                                                                                                               ==>  10 -1

       Question 1: What is the order of magnitude for the following numbers in (a), (b), (c), and (d)

          (a) 1.4 x10 – 4    (b) 6.5 x 10 4   (c) 5.6 x 10 -3      (d)  2.3 x10 5                         

     

    Decimal expression

    Scientific Notation

    Significant digits

    1,222,000.00

    1.222x106

    4

    1.22200000x106

    9

    0.00003350000

    3.45x10- 5

    3

    3.450000x10- 5

    7

    -9876543210

    -9.87654x109

    6

    -9.876543210x10-9

    10

    -0.0000000100

    -1 x10- 8

    1

    -1.00x10-8

    3

     

    4.Operation with significant figures

     Addition and subtraction

    Addition and Subtraction
    When measured quantities are used in addition or subtraction, the uncertainty is determined by the absolute uncertainty in the least precise measurement (not by the number of significant figures). Sometimes

    32.01 m  +  5.325 m + 12 m = 49.335 m but should be reported as 49 m because the number 12 m is the least precise measurement

     Multiplication and Division
    When experimental quantities are mutiplied or divided, the number of significant figures in the result is the same as that in the quantity with the smallest number of significant figures. If, for example, a density calculation is made in which 25.624 grams is divided by 25 mL, the density should be reported as 1.0 g/mL, not as 1.0000 g/mL or 1.000 g/mL.

    Example:

     Multiplication :   2.56 x 10 67 x (- 8.33 x 10 -54 )  =  - 2.13 x 10 14

    5.Scientifc Method

       In physics, we will observe the phenomenon, form a hypothesis, design and perform the experiment to test the hypothesis, examine the experimental results to confirm it repetition and consistency, and create models or theories to explain the results.

    Step 1: Observation and Ask questions

      Scientific method starts with observation. Observation is the process of using the senses of sight, touch, taste, hearing, and smell to gather the information about the world.     Observation can often lead to questions. For example, What causes a river to change its course ?

    Step 2: Form a hypothesis

      Once a question is asked and basic information has been gathered, a scientist may propose a tentative answer which is called the hypothesis. Most hypothesis is based on the known        facts about the similar events. The hypothesis offers a possible explanation or a solution to a problem.

    Step3: Test the hypothesis thru experiment

       Dependant variable and independent variable,

    Step4: Draw conclusion

      After many experiments and observations, a scientist may reach conclusions about the hypothesis. If the experimental results differ from what was expected, the hypothesis may be changed 

    Scientific model:

        An idea, equation, structure, and system cam model the phenomenon you are trying to explain. Scientific model is based on experimentation.

    Scientific law:

       It is a rule of nature that sums up related observations to describe a pattern in nature.

    Scientific theories:

       It is an explanation based on many observations supported by experimental results. Theories may serve as explanation for laws.

    6.Measurement,Precision versus Accuracy

    A measurement is a comparison between an unknown quantity and a standard. Accuracy refers to how closely a measured value agrees with the correct value.
    Precision refers to how closely individual measurements agree with each other.