PARADISE VALLEY COMMUNITY COLLEGE
SPRING SEMESTER, 2000
CHEMISTRY 130
SECTION 2230
DR. GERALD A. ROSENTHAL
UNITS OF MEASUREMENT
    A system  which permits standard, uniform measurement, based upon the European metric system-not that of the US, has been agreed upon for all scientific investigation and documentation. Known as Le Systéme International or SI, it acknowledges French contributions in establishing an international system of measure.

The fundamental units of the SI sytem are:
Mass                 kilogram        kg
Length               meter             m
Time                  second            s
Temperature     Kelvin            K
Current             ampere            A
Amount             mole                mol
Luminosity        candela           cd

The above seven parameters form the fundamental SI  of measurement.  All other terms such as a gram or centimeter are derived terms. Derived terms have their own importance and recognition but they are derived from one of the seven basic or fundamental units of the SI.
These derived units get their units from the fundamental units. An important derived unit in chemistry is the liter (L), which expresses volume. A liter is the volume that a cube with sides of 1 decimeter occupies. Thus, 1 L = 1 dm3
In a similar vein, one gram (gm) is one thousandth of a kilogram and one milligram is one thousandth of a gram.
Chemistry would be very difficult without the gram and milligram, but these are not fundamental units of the SI, that is reserved only for the kilogram.

The system of prefixes permits one to denote a wide range of variation in the magnitude of the fundamental and derived terms:
Common prefixes are:
For quantities less than unity: deci, centi, milli, micro, pico, and occasionaly femto are commonly used.  Work out the sizes of these unit prefixes.
For quantities more than unity, kilo, mega, giga, and tera are commonly used.  Work out the sizes for these unit prefixes.

Definitions of the Seven Basic S I Units

metre [m]
     The metre is the basic unit of length. It is the distance light travels, in a vacuum, in
     1/299792458th of a second.
kilogram [kg]
     The kilogram is the basic unit of mass. It is the mass of an international prototype in the form of
     a platinum-iridium cylinder kept at Sevres in France. It is now the only basic unit still
     defined in terms of a material object, and also the only one with a prefix[kilo] already
     in place.
second [s]
     The second is the basic unit of time. It is the length of time taken for 9192631770 periods of
     vibration of the caesium-133 atom to occur.
ampere [A]
     The ampere is the basic unit of electric current. It is that current which produces a specified
     force between two parallel wires which are 1 metre apart in a vacuum.It is named after the
     French physicist Andre Ampere (1775-1836).
kelvin [K]
     The kelvin is the basic unit of temperature. It is 1/273.16th of the thermodynamic temperature
     of the triple point of water. It is named after the Scottish mathematician and physicist
     William Thomson 1st Lord Kelvin (1824-1907).
mole [mol]
     The mole is the basic unit of substance. It is the amount of substance that contains as many
     elementary units as there are atoms in 0.012 kg of carbon-12.
candela [cd]
     The candela is the basic unit of luminous intensity. It is the intensity of a source of light of a
     specified frequency, which gives a specified amount of power in a given direction.

Derived Units of the S I

From the 7 basic units of the SI many other units are derived for a variety of purposes. Only some of them are explained here. The units printed in bold are either basic units or else, in some cases, are themselves derived.

hertz [Hz]
     The hertz is the SI unit of the frequency of a periodic phenomenon. One hertz indicates that 1
     cycle of the phenomenon occurs every second. For most work much higher frequencies are
     needed such as the kilohertz [kHz] and megahertz [MHz]. It is named after the German
     physicist Heinrich Rudolph Hertz (1857-94).
joule [J] (pronounced "jewel")
     The joule is the SI unit of work or energy. One joule is the amount of work done when an
     applied force of 1 newton moves through a distance of 1 metre in the direction of the force.It
     is named after the English physicist James Prescott Joule (1818-89).
newton [N]
     The newton is the SI unit of force. One newton is the force required to give a mass of 1
     kilogram an acceleration of 1 metre per second per second. It is named after the English
     mathematician and physicist Sir Isaac Newton (1642-1727).
pascal [Pa]
     The pascal is the SI unit of pressure. One pascal is the pressure generated by a force of 1
     newton acting on an area of 1 square metre. It is a rather small unit as defined and is more
     often used as a kilopascal [kPa]. It is named after the French mathematician, physicist
     and philosopher Blaise Pascal (1623-62).

The Prefixes of the S I

The S I allows the sizes of units to be made bigger or smaller by the use of appropriate prefixes. For
example, the electrical unit of a watt is not a big unit even in terms of ordinary household use, so it is
generally used in terms of 1000 watts at a time. The prefix for 1000 is kilo so we use kilowatts[kW]
as our unit of measurement. For makers of electricity, or bigger users such as industry, it is common
to use megawatts[MW] or even gigawatts[GW]. The full range of prefixes with their [symbols or
abbreviations] and their multiplying factors which are also given in other forms is

 
         peta  [P] 1 000 000 000 000 000                 = 10^15
        tera  [T] 1 000 000 000 000                     = 10^12
        giga  [G] 1 000 000 000                    (a thousand millions = a billion)
        mega  [M] 1 000 000                        (a million)
        kilo  [k] 1 000                            (a thousand)
        hecto [h] 100
        deca  [da]10
                  1
        deci  [d] 0.1
        centi [c] 0.01
        milli [m] 0.001                            (a thousandth)
        micro [µ] 0.000 001                        (a millionth)
        nano  [n] 0.000 000 001                    (a thousand millionth)
        pico  [p] 0.000 000 000 001                     = 10^-12
        femto [f] 0.000 000 000 000 001                 = 10^-15
        atto  [a] 0.000 000 000 000 000 001             = 10^-18
 

[µ] the symbol used for micro is the Greek letter known as 'mu'
Nearly all of the S I prefixes are multiples or sub-multiples of 1000. However, these are inconvenient
for many purposes and so hecto, deca, deci, and centi are also used.

Conventions of Usage in the S I
There are various rules laid down for the use of the SI and its units as well as some observations to
be made that will help in its correct use.

     Any unit may take only ONE prefix. For example 'millimillimetre' is incorrect and should be
     written as 'micrometre'.

     Most prefixes which make a unit bigger are written in capital letters (M G T etc.), but when
     they make a unit smaller then lower case (m n p etc.) is used. Exceptions to this are the kilo
     [k] to avoid any possible confusion with kelvin [K]; hecto [h]; and deca [da] or [dk]

     A unit which is named after a person is written all in lower case (newton, volt, pascal etc.)
     when named in full, but starting with a capital letter (N V Pa etc.) when abbreviated. An
     exception to this rule is the litre which, if written as a lower case 'l' could be mistaken for a '1'
     (one) and so a capital 'L' is allowed as an alternative. It is intended that a single letter will be
     decided upon some time in the future when it becomes clear which letter is being favoured
     most in use.

     Units written in abbreviated form are NEVER pluralised. So 'm' could always be either 'metre'
     or 'metres'. 'ms' could represent 'metre second' (whatever that is) or, more correctly,
     'millisecond'.

     An abbreviation (such as J N g Pa etc.) is NEVER followed by a full-stop unless it is the end
     of a sentence.

     To make numbers easier to read they may be divided into groups of 3 separated by spaces
     (or half-spaces) but NOT commas.

     The SI preferred way of showing a decimal fraction is to use a comma (123,456) to separate
     the whole number from its fractional part. The practice of using a point, as is common in
     English-speaking countries, is acceptable providing only that the point is placed ON the line of
     the bottom edge of the numbers (123.456).

     It will be noted that many units are eponymous, that is they are named after persons. This is
     always someone who was prominent in the early work done within the field in which the unit is
     used.


Uncertainty in Measurement
Because people can only measure something to a certain degree of accuracy, it is important to realize that a measurement always has some degree of uncertainty, which depends on the precision of the measureing device.

For example, if you weigh two heads of lettuce on a grocer's scale, the scale could show that both weigh 1.5 kg. But if you weigh the two on a balance, the balance may show that one weighs 1.488 kg while the other weighs 1.521 kg. So do the two heads have the same mass? Your conclusion depends on the certainty of those measurements. Therefore, it is important to indicate the uncertainty in any measurement. This is done by using SIGNIFICANT FIGURES.

Significant Figures
Rules for counting significant figures:
  1. Nonzero Integers: Nonzero integers always count as significant figures (i.e. three significant figures in the measurement 2.45 g).
  2. Zeros: There are three classes of zeros.
    1. Leading zeros are zeros that preceed all nonzero digits. They are never significant (i.e. 0.00057 has only two significant figures).
    2. Captive zeros are zeros between non zero digits. They are always significant (i.e. 90.08 has four significant figures).
    3. Trailing zeros are zeros at the right end of the number. They are significant only if the number contains a decimal point (i.e. 100 has only one signfiicant figure, but 1.00 x 102 has three significant figures).
  3. Exact Numbers: Numbers that are obtained by counting rather than measuring. They are assumed to have infinite significant figures. Numbers that arise from definitions are also exact (i.e. one inch is defined as exactly 2.54 centimeters, so that when 2.54 cm/in is used in a calculation, it will not limit the number of significant figures).
  4. Using Significant Figures in Calculations:
  1. Multiplication and Division: The number of significant figures in the result is the same as the number in the least precise measurement. For example:

    2. 4.28 x 8.3 = 35.524 before correction; after correction of significant figures, the result should be 36, since the limiting term (8.3) has only two significant figures.
  2. Addition and Subtraction: The result has the same number of decimal places as the least precise measurement used in the calculation. For example: 53.984 + 2.5 = 56.484 before correction; after correction, the result should be 56.5, since the limiting term has only one decimal place.