World of Chemistry

Chemistry 0010

Measurements

    Topics you should learn:

  1. Significant Figures and Units

  2. Scientific Notation

  3. Mass and Weight

  4. Dimensional Analysis Method of Problem Solving

Significant Figures and Units

When a scientist writes down a measurement, three kinds of information are being given:
  1. The magnitude of the measurement.
  2. The reliability of the number.
  3. The unit of the measurement.

The Magnitude and Reliability of the Measurement

Since all experimental measurements have uncertainties, we need to know how much we can trust the measurements. Let's illustrate the idea by considering the mass of an object measured on two different balances. Let's assume that the two balances are accurately calibrated. One measurement is taken on a "crude" balance, and the other is taken on a "sophisticated" balance. The table below shows us how to interpret the two masses.

crude balancesophisticated balance
Measurement 12.4 g 12.4536 g
Uncertainty of Measurment in the first decimal place in the fourth decimal place
Accuracy of Measurement to the first decimal place to the fourth decimal place
# of digits that are exact two; 12.4 five; 12.4536
# of digit that is uncertain one; 12.4 one; 12.4566

The measurement 12.4536 g is more accurate than the measurement 12.4 g. Using the sophisticated balance, we can report the mass of the object to four decimal places.

We can determine the number of significant figures for any measurement.

# of sig fig = # of digits that are EXACT + 1 final uncertain digit

  • 12.4536 g is a measurement with 6 significant figures.
  • 12.4 g is a measurement with 3 significant figures.

Given that the measuring tool is correctly calibrated, in general, a measurement that has more significant figures is the more accurate or reliable measurement.

Let's examine some simple rules in determining the number of significant figures in measurements that contains ZEROS,

  1. All nonzero digits are significant.
      4.0 430
  2. All zeros placed between significant digits are significant.
      4.0430
  3. All zeros at the end of a number and to the right of the decimal point are significant.
      4.0430
  4. All zeros at the end of a number and to the left of the assumed decimal point may or may not be significant.
  5. All zero digits to the left of the nonzero digit are not significant.They are used to locate the decimal point.
      0. 00002
The Units of the Measurements

A measurement without a unit is meaningless.

A MEASUREMENT MUST BE ACCOMPANIED BY A UNIT
Check out this site:
A Dictionary of Units
  • an explanation of the principal systems of units, their history, standards, and conversion factors for changing from one to the other.

    The Metric System

    • Read:
    • 2-2 - Measuring Matter (page 15)
    • 2-5 - Significant Digits (page 21)
    • 2-6 - Mathematical Operations involving Sig Figs (page 24)

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    Scientific Notation

    Scientists often use exponents to express very large and very small numbers.
    For example,

    Similarly,
    • 0.000001 can be written as 10-6
      • ten raised to the power of negative six
    Suppose we have a measurement of 6765.44 g and we wish to express this measurement in     scientific notation. We simply move the decimal over to the left until there is one digit (from 0 to 9 inclusive) to the left of the decimal point. Here, we move the decimal place three places to the left. Therefore, in scientific notation,

    6765.44 g = 6.76544 x 103 g.

    What about for a number like 750? Since this number is written without a decimal point, we cannot determine the number of significant figures. It can be 2 significant figures if you don't count the zero. Or, it can be 3 significant figures if you count the zero. To work around this problem, we use scientific notation:

    7.5 x 102 has 2 significant figures.
    7.50 x 102 has 3 significant figures.

    Read:
    • 2-7 - Exponents, Exponential Notation, and Scientific Notation
      (page 28)
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    Mass and Weight

    Check out this site:
    Weights and Measures "MegaConverter - The Web's Best Place to Figure What Equals What"
  • Resource for units, weights, measures and educational information on conversions and calculations.
    • Read:
    • 2-4 - Measuring Devices (page 20)
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    Dimensional Analysis of Problem Solving

    Many calculations in chemistry require that we convert quantities from one set of units to another. We can do this by using conversion factors. For examples,

    The basic setup for problem solving is:

    (information given) x (conversion factor(s)) = information sought

    Let's try to solve a problem using this basic setup.

    QUESTION: The density of a solid is 7.6 g/mL. What is its density in kg/L?

    What is the information sought? density in kg/L
    What is the information given? density in g/mL
    What conversion factor(s) are needed?

    Now we can organize the information and put it into a mathematical equation.

    Notice how we can cancel the unit "grams" because it occurs in the numerator and denominator. Likewise, we can cancel the unit" milliliters", and the number "1000". The units on the left-hand-side of the equation becomes kg/L, exactly the information sought.

    Unit Conversion

    Check out this site:
    Digital Generation - Unit Converter
  • Convert2, by Legacy Systems, is a WWW based, online tool for finding and converting scientific, engineering, and common units

    • Read:
    • 2-8 - Dimensional Analysis Method of Problem Solving
      for Conversions (page 33)
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    Rosamaría Fong, Instructor of Chemistry,
    British Columbia Institute of Technology, Burnaby, B.C. Canada.

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    All contents copyrighted © 1996
Rosamaría Fong, Instructor of Chemistry
All Rights reserved

    
: Last updated on June 7, 1996