Mathematical concepts for Food Technology (FPE20806)
Institution
Wageningen University (WUR)
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Mathematical concepts for Food Technology (FPE20806)
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1: Units, dimensions and quantities
–Dimension: a physical entity, which can be observed and/or measured (time, length, area,
volume, mass, force, temperature and energy).
–Unit: expresses the quantitative
magnitude of a dimension
(meter, centimeter, millimeter).
–SI: Système Internationale; an
international system of units
(right).
All dimensions can be
expressed in either a base
unit or a combination of
base units for derived units,
of which some have specific names:
1. Newton (N): The newton is the unit of force in kg*m*s-2.
2. Joule (J): The joule is the unit of energy in N*m.
3. Watt (W): The watt is the unit of power in J*s-1.
4. Pascal (Pa): The pascal is the unit of pressure in
N*m-2.
On the right a table with prefixes can be seen.
Prefixes are always put before the base
multiples of 10.
–Significant figures: include all nonzero digits and
non-terminal zeroes in a number.
–Terminal zero: 2360.
–Non-terminal zero: 0.0000206.
o 123 3 significant figures.
o 123.05 5 significant figures.
o 20.040 5 significant figures.
o 0.00240 3 significant figures.
o 2.500 2 significant figures better to use 2.5 * 103.
Rules for significance:
1. In addition or subtraction, the answer should not contain more significant digits than
the leas precise number.
Example: 1.030 + 1.3 + 1.4564 = 3.8.
The least precise number is 1.3, with one digit behind the decimal point, so the
answer should contain the same number of digits.
2. In multiplication or division, the number of significant digits in the answer should not
exceed that of the least precise original number.
, Example: 123 * 120 = 15000, if the terminal zero in 120 is not significant.
The least precise number has 2 significant figures, and the answer should also have 2
significant figures, so 15 kUnits.
3. When rounding off, raise the terminal significant number by one if the first of the
discarded digits start with 5 or lager; otherwise, the terminal significant figure
remains unchanged.
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