System of units

< Formulas question type

Writing unit symbols

In the Formulas question type, the writing of the units differs slightly from that in the SI because units are entered very simply on the computer. The rules for entering units are described below.

• The multiplication of unit symbols is indicated by a space, as prescribed in Section 5.1 of SI. The half-high (centred) dot (⋅) is not supported. For example, input 50 kN m, or 50 kN⋅m, as follows:
  

      

50 kN m

• Division of unit symbols is indicated by a solidus (oblique stroke, /) or by negative exponents.For example, input 10 m/s, or 10 m s^-1, as follows:
  

      

10 m/s

    or    

10 m s^(-1)

• Exponentiation is indicated by the circumflex accent (^, UTF-8 ﹠#94; or ASCII code 94 (alt+94)).For example, input 4.7 m², as follows:
  

      

4.7 m^2

• Parentheses are required when there is a risk of misinterpretation. For example, do not input 8 kN m^-2 but rather:

      

8 kN m^(-2)

• Permutations of the unit symbols are allowed. For example, the following two entries are considered identical:

      

3 m kg s^(-2)

    or    

3 kg m/s^2

Units

The system of units of the Formulas question type complies with the International System of Units (SI) (available free of charge). In the International System of Units (SI) units are classified as either base units or derived units (SI).

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.

There are seven base units in the SI:

Name	Symbol	Formulas question type input
metre	m	m
kilogram	kg	kg
second	s	s
ampere	A	A
kelvin	K	K
mole	mol	mol
candela	cd	cd

Coherent derived units are simple products of powers of base units. Some examples of coherent derived units are as follows:

Name	Symbol	Formulas question type Input from either column is acceptable
square meter	m2	m^2
cubic meter	m3	m^2
meter per second	m/s	m/s	m s^(-1)
meter per second squared	m/s2	m/s^2	m s^(-2)
reciprocal metre	m-1	m^(-1)
kilogram per cubic metre	kg/m3	kg/m^3	kg m^(-3)
kilogram per square metre	kg/m2	kg/m^2	kg m^(-2)
cubic metre per kilogram	m3/kg	m^3/kg	m^3 kg^(-1)
ampere per square metre	A/m2	A/m^2	A m^(-2)
etc.

Some coherent derived units have special names and symbols:

Name	Symbol	Formulas question type Input from either column is acceptable
radian	rad	rad		m/m
steradian	sr	sr		m^2/m^2
hertz	Hz	Hz		s^(-1)
newton	N	N		m kg s^(-2)
pascal	Pa	Pa	N/m^2	m^(-1) kg s^(-2)
joule	J	J	N m	m^2 kg s^(-2)
watt	W	W	J/s	m^2 kg s^(-3)
coulomb	C	C		s A
volt	V	V	W/A	m^2 kg s^(-3) A^(-1)
farad	F	F
ohm	Ω
siemens	S	S
weber	Wb	Wb
tesla	T	T
henry	H	H
degree Celcius	℃	℃
lumen	lm	lm
lux	lx	lx
becquerel	Bq
gray	Gy
sievert	Sv
katal	kat

The base and coherent derived units of the SI form a coherent set, designated the set of coherent SI units.

There are also units outside the SI. Non-SI units accepted for use with the SI are:

Name	Symbol	Formulas question type input
minute	min	min
hour	h	h
day	d	d
degree (plan angle)	°
minute (plan angle)	′
second (plan angle)	″
hectare	ha	ha
litre	L, l	L or l
tonne	t	t

Combined units

Under each Part _ on the Formulas question page, define Unit as single and combined units separated by =. For example:

Pa = N/m^2 = m^(-1) kg s^(-2)

SI Prefixes

The SI and Formula question prefixes are given in the table below.

Factor	Name	SI symbol	Formulas question input		Factor	Name	SI symbol	Formulas question input
101	deca	da	da		10-1	deci	d	d
102	hecto	h			10-2	centi	c	c
103	kilo	k	k		10-3	milli	m	m
106	mega	M	M		10-6	micro	μ	u
109	giga	G	G		10-9	nano	n	n
1012	tera	T	T		10-12	pico	p	p
1015	peta	P	P		10-15	femto	f	f
1018	exa	E	E		10-18	atto	a
1021	zetta	Z			10-21	zepto	z
1024	yotta	Y	Y		10-24	yocto	y

, togeher with the Formulas question prefixes:

An alternative syntax can be used: a single unit followed by a list of SI prefix names. For example:

W: k M G T;

which is equivalent to 1 W = 1e-3 kW = 1e-6 MW = 1e-9 GW = 1e-12 TW.

Conversion rules

Conversion rules allow students to use alternative units.

Common conversion rules

Under Extra Options on the Formulas question page, for / [Global - Basic conversion rules], select '"Common SI unit"' in order to use predefined common SI units conversion rules. With this setting, the following answers are equivalent:

5 s
5000 ms
5e9 ns

        

0.2 m/s
200 mm/s
 

        

1 m^2
10000 cm^2
1e-6 km^2

Select None if the Common SI unit contradicts your custom rules.

Custom rules

The conversion of single units can be specified by equating their values. For example:

1 m = 100 cm = 1000 mm;
1 cm = 0.3937 inch;

With the above conversion rule, the following answers are equivalent:

10 inch
25.4 cm
254 mm
0.254 m

See the file conversion_rules.php.

Marking

The system of units allows to test students' knowledge of units. Alternative equivalent units are allowed.

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).

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.

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.

< Formulas question type