Review Part 1 Nov. 30, 2004

Chapter 1 Intro to Physics


  • Physics is the study of the physical world, from motion and energy to light and electricity. Physics is the most basic science.

  • Physics uses the scientific method to discover general laws that can be used to make predictions about a variety of situations.

  • Understand the steps of the scientific method.

    A common technique in physics for analyzing a complex situation is to disregard irrelevant factors and create a model that describes the essence of a system or situation.

  • Physics measurements are typically made and expressed in Systeme International, SI, a system that uses a set of base units and prefixes to describe measurements of physical quantities. Know the units of length, mass, time, and force in the SI system, the cgs system and the Avoirdupois system. Know the units of energy and power in the SI system.

  • Accuracy describes how close a measurement is to reality. Precision results from the limitations of the measuring device used.

  • Significant figures are sometimes called significant digits and are used to indicate which digits in a measurement are actual measurements.

  • Significant-figure rules provide a means to ensure that calculations do not report results that are more precise than the data used to make them.
    Know Rules for determining the number of significant digits.
    Know Rules for adding or subtracting the number of significant digits.
    Know Rules for multiplying or dividing the number of significant digits.

    Rules for determining the number of significant digits in a number. (Significant digits or figures are shown in red)

    Rule 1. All nonzero integers are significant.
    445 cm has 3 significant figures
    445 cm.
    Rule 2. All zeros to the left of the first nonzero digit are not significant since they are used to locate the decimal point.
    0.00445 kg has 3 significant figures
    0.00    445 kg.
    Rule 3. All zeros between nonzero digits are significant.
    2100.09 cm has 6 significant figures
     2100.09 cm.
    0.0401 L has 3 significant figures
    0.0    401 L
    Rule 4. All zeros at the end of a number that has a decimal point are significant.
    34.070 mg has 5 significant figures
    34.070 mg
    0.0670 g has 3 significant figures
    0.0    670 g.
    400. mm has 3 significant figures
    400. mm.
    Rule 5. Zeros at the end of a whole number that has no decimal point is confusing since they may or may not be significant.
    8000 L
    The measurement written as 8000 L is confusing.
    Our text assumes 8000 L to have 4 significant figures.


    Rules for adding or subtracting the number of significant digits.
    I. Add (or subtract)
    Step 1. Find number of digits to the right of the decimal for each number.
    Step 2. Pick out the least number of digits to the right of the decimal for each number, and call this number L.
    Step 3. Add (or subtract) the numbers to get your answer.
    Step 4. Adjust your answer to have L number of digits to the right of the decimal.

    Example:
    Add 91.3 and 5.86,
    Step 1. Find number of digits to the right of the decimal for each number.
    91.3 has 1 digit to the right of the decimal.
    5.86 has 2 digits to the right of the decimal.
    Step 2. Pick out the least number of digits to the right of the decimal for each number, and call this number L.
    1 is the least number of digits to the right of the decimal, so
    L = 1.
    Step 3. Add the numbers to get your answer.
    91.3
    +5.86
    97.16
    Step 4. Adjust your answer to have L number of digits to the right of the decimal.
    Now L = 1, so to have 1 digit to the right of the decimal, you round up 97.16 to 97.2.
    To put the answer in scientific notation 97.2 = 9.72 x 10.
    Rules for multiplying or dividing the number of significant digits.
    II. To multiply (or divide) numbers
    Step 1. Find the number of significant digits in each number.
    Step 2. Pick out the smallest number of significant digits for these numbers, and call this number S.
    Step 3. Multiply (or divide) the numbers to get your answer.
    Step 4. Adjust your answer to have S number of significant digits.

    Example:
    Multiply 231.0 and 0.12,
    Step 1. Find number of significant digits in each number.
    231.0 has 4 significant digits.
    0.12 has 2 significant digits.
    Step 2. Pick out the smallest number, and call this number S.
    2 is the smallest number of significant digits, so
    S = 2.
    Step 3. Multiply the numbers to get your answer.
    231.0
    x 0.12
     27.72
    Step 4. Adjust your answer to have S number of significant digits.
    Now S = 2, so adjust the answer (27.72) to have 2 significant digits.
    28. (or 2.8 x 10 ) is your final answer.
    To put the answer in scientific notation: 28. = 2.8 x 10.

    For a = 3.23 b= 2002.674 c = 3.2 x 108 d = 0.11 x 10-14, calculate and put the answer in scientific notation:

    1. a + b = _________ 4. c X d = _________

    2. a - b = _________ 5. c divided by d = _________

    3. a X c = _________

    see links in the Physics section associated with significant digit homework.