Measurements

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Units of Measurement

In order for people around the world to agree on quantiative observations, a system of measurement must be defined. Today, scientists worldwide agree on the SI (le Systéme International) system, also known as the metric system.

The fundamental units of the SI sytem are:
Physical QuanitityName of UnitAbbreviation
Mass kilogram kg
Length meter m
Time second s
Temperature Kelvin K
Electric current ampere A
Amount of substance mole mol
Luminous intensity candela cd
But since the fundamental units are not always convenient (i.e. expessing the mass of a sheet of paper in kilograms is ridiculous), prefixes are used to change the size of the unit.

Common prefixes are:
PrefixSymbolFactor
exa E 1018
peta P 1015
tera T 1012
giga G 109
mega M 106
kilo k 103
hecto h 102
deka da 101
--- --- 100
deci d 10-1
centi c 10-2
milli m 10-3
micro mu10-6
nano n 10-9
pico p 10-12
femto f 10-15
atto a 10-18
For example, 1000 meters (or 103 m) can be expressed as 1 km (kilometer).

In addition to fundamental units, there are also derived units, which 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 dm (decimeter) takes up. In other words, 1 L = 1 dm3.

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 bathroom scale, the bathroom scale may 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).
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:
    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.
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