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| [https://docs.moodle.org/33/en/Formulas_question_type < Formulas question type] | | #REDIRECT [[Formulas:_Systems_of_units]] |
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| ==Marking==
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| The system of units allows to test students' knowledge of units. Alternative equivalent units are allowed.
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| You can specify mark fraction deduction for a wrong unit. The wrong unit here means that the unit that is not convertible to the correct unit, under conversion rules. Suppose a student get 2 marks for this subquestion answer. If the unit penalty = 0.2 and she give wrong unit, then the student can get 2(1-0.2) = 1.6 mark for this submission. (See Grading scheme).
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| If a teacher does not specify any unit for the subquestion, then the unit box will not be displayed and there is no need for students to enter it. However, if the student enters anything after their answer, it is usually considered to be incorrect so the mark of unit will be deduced. Hence, in the above case, it is better to set 1 for mark deduction.
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| Nevertheless, if you do not want to penalize the student entering arbitrary string at the end of answer, set 0 for mark deduction. i.e. their unit does not count toward their grade, but you still allow student use any convertible unit. Note that you have assumed a default answer that does not require unit.
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| ==Units==
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| In the International System of Units (SI) units are classified as either base units or derived units ([https://www.bipm.org/en/publications/si-brochure/ SI]).
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| There are seven base units:
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| {| class="nicetable"
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| |-
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| ! Name
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| ! Symbol
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| |-
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| | metre
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| | m
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| |-
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| | kilogram
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| | kg
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| |-
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| | second
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| | s
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| |-
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| | ampere
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| | A
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| |-
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| | kelvin
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| | K
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| |-
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| | mole
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| | mol
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| |-
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| | candela
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| | cd
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| |}
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| Coherent derived units are simple products of powers of base units. Some examples of coherent derived units are as follows:
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| {| class="nicetable"
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| |-
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| ! Name
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| ! Symbol
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| |-
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| | square meter
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| | m<sup>2</sup>
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| |-
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| | cubic meter
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| | m<sup>3</sup>
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| |-
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| | meter per second
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| | m/s
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| |-
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| | meter per second squared
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| | m/s<sup>2</sup>
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| |-
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| | reciprocal metre
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| | m<sup>-1</sup>
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| |-
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| | kilogram per cubic metre
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| | kg/m<sup>3</sup>
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| |-
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| | kilogram per square metre
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| | kg/m<sup>2</sup>
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| |-
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| | cubic metre per kilogram
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| | m<sup>3</sup>/kg
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| |-
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| | ampere per square metre
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| | A/m<sup>2</sup>
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| |-
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| | etc.
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| |}
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| Some coherent derived units have special names and symbols:
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| {| class="nicetable"
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| |-
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| ! Name
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| ! Symbol
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| |-
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| | radian
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| | rad
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| |-
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| | steradian
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| | sr
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| |-
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| | hertz
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| | Hz
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| |-
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| | newton
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| | N
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| |-
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| | pascal
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| | Pa
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| |-
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| | joule
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| | J
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| |-
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| | watt
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| | W
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| |-
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| | coulomb
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| | C
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| |-
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| | volt
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| | V
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| |-
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| | farad
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| | F
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| |-
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| | ohm
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| | Ω
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| |-
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| | siemens
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| | S
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| |-
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| | weber
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| | Wb
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| |-
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| | tesla
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| | T
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| |-
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| | henry
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| | H
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| |-
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| | degree Celcius
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| | ℃
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| |-
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| | lumen
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| | lm
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| |-
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| | lux
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| | lx
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| |-
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| | becquerel
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| | Bq
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| |-
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| | gray
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| | Gy
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| |-
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| | sievert
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| | Sv
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| |-
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| | katal
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| | kat
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| |}
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| The base and coherent derived units of the SI form a coherent set, designated the set of coherent SI units.
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| There are also units outside the SI. Non-SI units accepted for use with the SI are:
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| {| class="nicetable"
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| |-
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| ! Name
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| ! Symbol
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| |-
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| | minute
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| | min
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| |-
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| | hour
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| | h
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| |-
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| | day
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| | d
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| |-
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| | degree (plan angle)
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| | °
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| |-
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| | minute (plan angle)
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| | ′
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| |-
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| | second (plan angle)
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| | ″
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| |-
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| | hectare
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| | ha
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| |-
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| | litre
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| | L, l
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| |-
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| | tonne
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| | t
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| |}
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| Units of the Formulas question type system of units are the same as those of the set of coherent SI units and as the units outside the SI. The writing of the units differs slightly because they are entered very simply on the computer.
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| Note that the ordering of base unit is not important.
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| For a given physical quantity, the unit name can be entered using the following rules:
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| Base unit: e.g. length (m), it should be simply entered as m
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| Positive exponent: e.g. area (m2), it should be entered as m^2.
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| Negative exponent: e.g. wavenumber (m-1), it should be entered as m^(-1).
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| Compose unit: e.g. velocity (m s-2), it should be entered as m s^(-2) with the base unit separated by the space (representing multiplication).
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| Alternative for negative exponent: One preceding division operator can also be used, say m/s^2 which is equivalent to m s^(-2).
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| Students need to enter the same format for unit (i.e. they need to know the above rule). Examples:
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| Unit Description
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| m a base unit, meter, for the dimension length
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| kg a base unit, kilogram, for the dimension mass
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| N a base unit (it is called derived unit in SI), newton, for the physical quantity force
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| m/s a composite unit, for the physical quantity velocity
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| kg m/s^2 a composite unit, with the same dimension as newton
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| Examples of answers with unit:
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| 1 m
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| 0.1 m^2
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| 20 m s^(-1)
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| 400 kg m/s
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| 100 kW
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| ==Conversion rules==
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| Conversion rules allow students to use alternative units. (See UnitConversion for details.)
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| ====Other rules====
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| You can specify the conversion of the base unit by equating their values under different units. Examples:
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| <pre style="font-size:113%;">
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| 1 m = 100 cm = 1000 mm;
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| 1 cm = 0.3937 inch;
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| </pre>
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| With the above conversion rule, the following answers are equivalent:
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| <pre style="color:#f98012;font-size:113%;">
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| 10 inch
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| 25.4 cm
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| 254 mm
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| 0.254 m
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| </pre>
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| For the SI prefix, an alternative syntax can be used: base unit followed by a list of SI prefix name.
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| <pre style="color:#f98012;font-size:113%;">W: k M G T;</pre>
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| which is equivalent to <span style="font-family: monospace;color:#f98012;font-size:113%;">1 W = 1e-3 kW = 1e-6 MW = 1e-9 GW = 1e-12 TW</span>.
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| ===Basic conversion rule===
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| For the conversion between common SI unit with different prefix, there are a set of predefined conversion rules for them. The only thing you need to do is to choose the 'Common SI unit' in the 'Basic conversion rule'.
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| The following answers in the each group
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| 5 s
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| 5000 ms
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| 5e9 ns
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| 0.2 m/s
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| 200 mm/s
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| 1 m^2
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| 10000 cm^2
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| 1e-6 km^2
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| are all equivalent to each other. So if one of the answer is correct, all other are also correct answers.
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| Note that you may also use 'None' if you find it contradicting with your own rules. If you want to define you own, see the file conversion_rules.php.
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| Identifying composite unit: Note that, the base units and composite unit cannot be identified in the conversion rules above. To specify a list of allowable composite unit, you can use separator '=' in the 'Unit'. For example
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| N = kg m s^(-2)
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| It identity the unit Newton to its SI counterpart. Hence, both composite unit are correct.
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| [https://docs.moodle.org/33/en/Formulas_question_type < Formulas question type]
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