System of units: Difference between revisions
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===[Global] - Basic conversion rule field=== | ===[Global] - Basic conversion rule field=== | ||
Select | Select a basic conversion rule. Prefixes and conversion factors for different basic rules are defined in the flle '''conversion_rules.php'''. In the file downloaded from the '''Moodle plugins directory''', two rules are defined: '''None''' and '''Common SI units'''. | ||
In the file downloaded from the | |||
====None==== | ====None==== | ||
Select '''None''' if | Select '''None''' if other rules contradicts the rule defined in '''[Global] - Basic conversion rule''' if any. | ||
====Common SI units==== | |||
'''Common SI | The '''Common SI units''' rule defines prefixes and conversion factors commonly used by physicists. The rule is as follows: | ||
<pre style="font-size:113%;"> | <pre style="font-size:113%;"> | ||
//Prefixes | |||
m: k d c m u n p f; | m: k d c m u n p f; | ||
s: m u n p f; | s: m u n p f; | ||
Line 117: | Line 114: | ||
T: k m u n p; | T: k m u n p; | ||
H: k m u n p; | H: k m u n p; | ||
//Conversion factors | |||
J = 6.24150947e+18 eV; | |||
</pre> | </pre> | ||
Note that, for example, <span style="font-family:monospace;font-size:113%;">m: k c d m u n p f;</span> is equivalent to: | Note that, for example, <span style="font-family:monospace;font-size:113%;">m: k c d m u n p f;</span> is equivalent to: | ||
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<pre style="font-size:113%;">1 m = 1e-3 km = 1e1 dm = 1e2 cm = 1e3 mm = 1e6 um = 1e9 nm = 1e12 pm = 1e15 fm;</pre>. | <pre style="font-size:113%;">1 m = 1e-3 km = 1e1 dm = 1e2 cm = 1e3 mm = 1e6 um = 1e9 nm = 1e12 pm = 1e15 fm;</pre>. | ||
=====Example===== | |||
With the '''Common SI units''' rule, the following answers are equivalent: | |||
<pre style="font-size:113%;"> | <pre style="font-size:113%;"> | ||
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</pre> | </pre> | ||
As these prefixes and conversion factors concern mainly physicists, the rule could be renamed '''Physics Units'''. | |||
==Writing unit symbols== | ==Writing unit symbols== |
Revision as of 01:15, 31 October 2017
Defining 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;
Add conversions of single units by equating their values.
Example
1 m = 39.3700787 in;
With the above conversion rule, the following answers are equivalent:
10 in 0.254 m 25.4 cm 254 mm
[Global] - Basic conversion rule field
Select a basic conversion rule. Prefixes and conversion factors for different basic rules are defined in the flle conversion_rules.php. In the file downloaded from the Moodle plugins directory, two rules are defined: None and Common SI units.
None
Select None if other rules contradicts the rule defined in [Global] - Basic conversion rule if any.
Common SI units
The Common SI units rule defines prefixes and conversion factors commonly used by physicists. The rule is as follows:
//Prefixes 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; //Conversion factors J = 6.24150947e+18 eV;
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;
.
Example
With the Common SI units rule, 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
As these prefixes and conversion factors concern mainly physicists, the rule could be renamed Physics Units.
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
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 activitiesWikipedia, 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):
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 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 |
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
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.