System of units

< Formulas question type

Setting units

Units are defined on the Formulas question page, in the following three places:

• For each part, in the Unit field.
• For each part, in the Other rules field.
• Under Extra options, in the [Global] - Basic conversion rule field.

Unit field

Specify a single or a combined unit.

Example

kg

N

m/s^2

You can also specify single and combined units separated by =.

Example

In order to accept N and kg m/s² as valid units, define Unit as follows:

N = kg m/s^2

Note that /s^2 must be placed at the end of the unit. Hence,  N = /s^2 kg m   and   N = kg /s^2 m   will lead to an error.

With the above setting, the following units will be considered correct:

N
kg m/s^2
kg m /s^2
m kg /s^2
m kg s^(-2)
s^(-2) kg m
s^(-2) m kg

Example

In order to accept W, J/s and m² kg s^-3 as valid units, specify:

W = J/s = m^2 kg s^(-3)

Other rules field

Add prefixes that are not defined in the [Global] - Basic conversion rule by writing units followed by a list of prefixes.

Example

Specify that meganewton (MN) is an acceptable unit by writing the following:

N: M;

Writing unit symbols

In the Formulas question, 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 in the Formulas question 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 (≡ 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

Unit symbols are case sensitive. For example, kilonewton is written kN, not KN, kn or Kn.

Units

The International System of Units (SI, from the French Système international (d'unités)) is the most widely used system of measurement. It has now been adopted accross the world, except in Liberia, Myanmar and the United States. The US is the only industrialized nation that does not mainly use the SI in its commercial and standards activities^{Wikipedia, International System of Units}. The SI is available here, free of charge. (The English version follows the French version.)

In the SI, units are classified as follows (with reference to the table in the SI):

• Base units (Table 1)
• Coherent derived units (Table 2)
• Coherent derived units with special names and symbols (Table 3)

Note that coherent derived units can include coherent derived units with special names and symbols (Table 4)

• Non-SI units accepted for use with the SI (Table 6)
• Non-SI units whose values in SI units must be obtained experimentally (Table 7)
• Other non-SI units (Table 8)
• Non-SI units associated with the CGS and the CGS-Gaussian system of units (Table 9)
• Other non-SI units not recommended of use (including the British imperial system and the United States customary system of units)

Conversion factors for the later units are available from the US National Institute of Standards and Technology (NIST):

• listed alphabetically
• listed by kind of quantity or field of science

SI base units

There are seven base units in the SI:

Name	Symbol	Formulas question 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

Coherent derived units are products of powers of base units, without a numerical factor. Some examples of coherent derived units are as follows:

Name	Symbol	Formulas question 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.

Coherent derived units with special names and symbols

Some coherent derived units have special names and symbols:

Name	Symbol	Formulas question Input from either column is acceptable
radian	rad	rad
steradian	sr	sr
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

Non-SI units accepted for use with the SI are:

Name	Symbol	Formulas question 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

SI Prefixes

The SI and Formulas question prefixes are given in the table below. The only difference between the two systems is that the prefix micro is written μ in the SI but entered as u in the Formulas question.

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	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	a
1021	zetta	Z	Z		10-21	zepto	z	z
1024	yotta	Y	Y		10-24	yocto	y	y

---

Formulas question system of units

The system of units of the Formulas question type complies with the SI. Formula question units can be any of all the units mentioned above, i.e. SI units and non-SI units.

Formulas question units can be either single or combined.

Formulas question unit	Type	Examples
		Name of unit	SI symbol	Formulas question input
Single (i.e. individual) unit	SI base unit	meter	m	m
		kilogram	kg	kg
		second	s	s
	Coherent derived SI units with special names and symbols	hertz	Hz	Hz
		newton	N	N
		pascal	Pa	Pa
	Non-SI units accepted for use with the SI	minute	min	min
		hour	h	h
		day	d	d
	Non-SI units whose values in SI units must be obtained experimentally	electronvolt	eV	eV
		dalton	Da	Da
		unified atomic mass unit	u	u
	Other non-SI units	bar	bar	bar
		millimetre of mercury	mmHg	mmHg
		ångström	Å	Å (Ascii 143)
	Non-SI units associated with the CGS and the CGS-Gaussian system of units	erg	erg	erg
		dyne	dyn	dyn
		poise	P	P
	Other non-SI units not recommended for use	barrel of oil	bbl	bbl
		inch	inch	in
		foot	ft	ft
Combined unit (any combination of single units)	All types	square meter	m2	m^2
		meter per second	m/s	m/s
		meter per second squared	m/s2	m/s^2
		hertz expressed in terms of SI base units	s-1	s^(-1)
		newton expressed in terms of SI base units	m kg s-2	m kg s^(-2)
		pascal expressed in terms of SI base units	m-1 kg s-2	m^(-1) kg s^(-2)
		pascal second	Pa s	Pa s
		radian per second squared	rad/s2	rad/s^2
		watt per square metre steradian	W/(m2 sr)	W/(m^2 sr)
		poise expressed in terms of CGS units	dyn s cm-2	dyn s cm^(-2)
		foot pound	ft lb	ft lb
		pound per inch squared	lb/in2	lb/in^2
		Btu per hour	Btu/h	Btu/h

Physics units

Physics units are defined as Common SI units in the file conversion_rules.php. In the downloaded file, Common SI units prefixes are as follows:

m: k d c m u n p f;
s: m u n p f;
g: k m u n p f;
mol: m u n p;
N: k m u n p f;
A: m u n p f;
J: k M G T P m u n p f;
eV: k M G T P m u;
W: k M G T P m u n p f;
Pa: k M G T P;
Hz: k M G T P E;
C: k m u n p f;
V: k M G m u n p f;
ohm: m k M G T P;
F: m u n p f;
T: k m u n p;
H: k m u n p;

As these units concern mainly physicists, they might be renamed Physics Units in future versions of the plugin.

Note that, for example, m: k c d m u n p f; is equivalent to:

1 m = 1e-3 km = 1e1 dm = 1e2 cm = 1e3 mm = 1e6 um = 1e9 nm = 1e12 pm = 1e15 fm;

.

Under Extra Options on the Formulas question page, for [Global - Basic conversion rules], select Common SI unit in order to use these prefixes. 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.

Other prefixes

In a particular context, not all prefixes are used with units. For example, in construction engineering, kilonewtons (kN) et meganewtons (MN) are used, but not millinewtons (mN).

The file conversion_rules.php can be edited and default Common SI units prefixes modified. Other rules can also be defined in the file conversion_rules.php.

Prefixes can also be added to units in the Other rules fields of each Part _, on the Formulas question page. For example, adding N: M; allows using MN.

Conversion

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

Conversion rules can be defined together with prefixes in the file conversion_rules.php. In the downloaded file, the only conversion rule defined under Common SI units is the following:

J = 6.24150947e+18 eV;

As with prefixes, conversion rules can also be defined in the Other rules field of each Part _, on the Formulas question page.

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