Differences

This shows you the differences between two versions of the page.

--- manual:chapter3:units [2018/10/25 10:17]
claudio [Operating with Units]
+++ manual:chapter3:units [2019/09/18 16:30]
jojo1973 [Multiples and Submultiples]
@@ Line 22: / Line 22: @@
 Exponents within a unit expression can be integer numbers, real numbers or fractional exponents. The use of fractional exponents is always preferred over real numbers because they can be simplified in an exact way. \\
 ''3_[m^(2/3)]'' is always preferred to ''3_[m^0.666667]'' \\
+==== Multiples and Submultiples ====
+Multiples and submultiples of many units are obtained by prefixing them with the standard SI prefixes. Therefore, ''1_dal'' is equivalent to ''10_l'' and ''3.5_MHz'' is equivalent to ''3500000_Hz''.
+There is only one exception: prefixes can't be used if the resulting name matches an already existing unit. For example, it's not possible use ''_[min]'' to mean milliinches because ''_[min]'' is already defined and corresponds to the time unit "minute".
+^  SI Prefix  ^  Factor  ^  Name  ^
+|  Y   |  $10^{24}$   |  yotta-  |
+|  Z   |  $10^{21}$   |  zetta-  |
+|  E   |  $10^{18}$   |  exa-    |
+|  P   |  $10^{15}$   |  peta-   |
+|  T   |  $10^{12}$   |  tera-   |
+|  G   |  $10^{9}$    |  giga-   |
+|  M   |  $10^{6}$    |  mega-   |
+|  k   |  $10^{3}$    |  kilo-   |
+|  h   |  $10^{2}$    |  hecto-  |
+|  da  |  $10^{1}$    |  deka-   |
+|  d   |  $10^{-1}$   |  deci-   |
+|  c   |  $10^{-2}$   |  centi-  |
+|  m   |  $10^{-3}$   |  milli-  |
+|  µ   |  $10^{-6}$   |  micro-  |
+|  n   |  $10^{-9}$   |  nano-   |
+|  p   |  $10^{-12}$  |  pico-   |
+|  f   |  $10^{-15}$  |  femto-  |
+|  a   |  $10^{-18}$  |  atto-   |
+|  z   |  $10^{-21}$  |  zepto-  |
+|  y   |  $10^{-24}$  |  yocto-  |
 ==== Operating with Units ====
@@ Line 34: / Line 62: @@
 To extract the value part of a unit object, use the ''UVAL'' command, which will return the object without its unit.
 ==== Custom Units ====
@@ Line 72: / Line 101: @@
 | 1_ftUS | surveying foot | 1_ftUS = 1200/3937_m | US surveying length |
 | 1_mil | thousandth of inch | 1_mil = 0.001_in | US customary length |
-| 1_µ | micron or micrometre | 1_µ = 1_µm | SI length |
+| 1_µ | micron | 1_µ = 1_µm | SI length |
-| 1_Å | Ångström | 1_Å = 0.1_nm | non-SI length |
+| 1_Å | ångström | 1_Å = 0.1_nm | non-SI length |
-| 1_fermi | fermi or femtometre | 1_fermi = 1_fm | SI length |
+| 1_fermi | fermi  | 1_fermi = 1_fm | SI length |
 | **Area** ||||
@@ Line 106: / Line 135: @@
 | 1_cu | cup | 1_cu = 1/16_gal | US customary volume |
 | 1_ozfl | fluid ounce | 1_ozfl = 1/128_gal | US customary volume |
-| 1_tbsp | table spoon | 1_tbsp = 1/2_ozfl | US customary volume |
+| 1_tbsp | tablespoon | 1_tbsp = 1/2_ozfl | US customary volume |
-| 1_tsp | tea spoon | 1_tsp = 1/6_ozfl | US customary volume |
+| 1_tsp | teaspoon | 1_tsp = 1/6_ozfl | US customary volume |
 | 1_fbm | board foot | 1_fbm = 144_in%%^%%3 | US customary volume |
 | 1_galUK | gallon (UK) | 1_galUK = 0.00454609_m%%^%%3 | Imperial volume |
@@ Line 127: / Line 156: @@
 | **Time** ||||
 | Unit | Unit name | Definition | Description |
-| 1_yr | tropical year | 1_yr = 31556925.9747_sper  | 1952 Ephemeris Time |
+| 1_yr | tropical year | 1_yr = 31556925.9747_s  |  per 1952 Ephemeris Time |
 | 1_d | day | 1_d = 86400_s | SI time |
 | 1_h | hour | 1_h = 3600_s | SI time |
 | 1_min | minute | 1_min = 60_s | SI time |
 | 1_s | second | 1_s | Base SI unit of time |
-| 1_Hz | Hertz | 1_Hz = 1_1/s | SI frequency |
+| 1_Hz | hertz | 1_Hz = 1_1/s | SI frequency |
 | **Speed** ||||
@@ Line 158: / Line 187: @@
 | Unit | Unit name | Definition | Description |
 | 1_kg | kilogram | 1_kg | Base SI unit of mass |
-| 1_g | kilogram | 1_g = 0.001_kg | SI mass |
+| 1_g | gram | 1_g = 0.001_kg | SI mass |
 | 1_lb | pound | 1_lb = 7000_grain | US customary mass |
 | 1_oz | ounce | 1_oz = 1/16_lb | US customary mass |
@@ Line 165: / Line 194: @@
 | 1_ton | tonne | 1_ton = 2000_lb | US customary mass |
 | 1_tonUK | tonne (UK) | 1_tonUK = 2240_lb | Imperial mass |
-| 1_t | Metric tonne | 1_t = 1000_kg | non-SI mass |
+| 1_t | metric tonne | 1_t = 1000_kg | non-SI mass |
 | 1_ozt | troy ounce | 1_ozt = 480_grain | Imperial mass |
-| 1_ct | Metric carat | 1_ct = 200_mg | Metric System mass |
+| 1_ct | metric carat | 1_ct = 200_mg | Metric System mass |
 | 1_grain | grain | 1_grain = 64.79891_mg | Imperial mass |
 | 1_u | unified atomic mass | 1_u = 1.660539040E-27_kg | non-SI mass |
 | 1_mol | mole | 1_mol | Base SI amount of substance |
 | 1_gmol | gram mole | 1_gmol = 1_mol | non-SI amount of substance |
-| 1_lbmol | pound mole | 1_lbmol = 453.59237_mol | US customary substance |
+| 1_lbmol | pound mole | 1_lbmol = 453.59237_mol | US customary amount of substance |
 | **Force** ||||
 | Unit | Unit name | Definition | Description |
-| 1_N | Newton | 1_N = 1_kg*m/s%%^%%2 | SI force |
+| 1_N | newton | 1_N = 1_kg*m/s%%^%%2 | SI force |
 | 1_dyn | dyne | 1_dyn = 1_g*cm/s%%^%%2 | non-SI force |
 | 1_gf | gram-force | 1_gf = 1_g*ga | non-SI force |
 | 1_kip | kip | 1_kip = 1000_lbf | US customary force |
 | 1_lbf | pound-force | 1_lbf = 1_lb*ga | US customary force |
-| 1_pdl | poundal | 1_pdl = = 1_lb*ft/s%%^%%2 | US customary force |
+| 1_pdl | poundal | 1_pdl = 1_lb*ft/s%%^%%2 | US customary force |
 | **Energy** ||||
 | Unit | Unit name | Definition | Description |
-| 1_J | Joule | 1_J = 1_N*m | SI energy |
+| 1_J | joule | 1_J = 1_N*m | SI energy |
 | 1_kW*h | kilowatt-hour | 1_kW*h = 3.6_MJ | non-SI energy |
 | 1_erg | erg | 1_erg = 1_dyn*cm | non-SI energy |
-| 1_kcal | kilo calorie | 1_kcal = 1000_cal | non-SI energy |
+| 1_kcal | kilocalorie (thermochemical) | 1_kcal = 1000_cal | non-SI energy |
-| 1_cal | calorie | 1_cal = 4.184_J | non-SI energy |
+| 1_cal | calorie (thermochemical) | 1_cal = 4.184_J | non-SI energy |
 | 1_Btu | british thermal unit | 1_Btu = =1055.056_J | Imperial energy |
 | 1_ft*lbf | foot-pound | 1_ft*lbf = 1_lb*ft*ga | US customary energy |
 | 1_therm | therm | 1_therm = 100000_Btu | Imperial energy |
-| 1_MeV | mega electronvolt | 1_MeV = 1E6_eV | non-SI energy |
+| 1_MeV | megaelectronvolt | 1_MeV = 1E6_eV | non-SI energy |
 | 1_eV | electronvolt | 1_eV = 1.6021766208E-19_J | non-SI energy |
 | **Power** ||||
 | Unit | Unit name | Definition | Description |
-| 1_W | Watt | 1_W = 1_J/s | SI power |
+| 1_W | watt | 1_W = 1_J/s | SI power |
 | 1_kW | kilowatt | 1_kW = 1000_W | SI power |
 | 1_MW | megawatt | 1_MW = 1000000_W | SI power |
@@ Line 206: / Line 235: @@
 | **Pressure** ||||
 | Unit | Unit name | Definition | Description |
-| 1_Pa | Pascal | 1_Pa = 1_N/m%%^%%2 | SI pressure |
+| 1_Pa | pascal | 1_Pa = 1_N/m%%^%%2 | SI pressure |
 | 1_atm | atmospheric pressure | 1_atm = 101325_Pa | non-SI pressure |
 | 1_bar | bar | 1_bar = 100000_Pa | non-SI pressure |
 | 1_psi | pound per square inch | 1_psi = 1_lbf/in%%^%%2 | US customary pressure |
-| 1_Torr | Torricelli | 1_Torr = 1/760_atm | non-SI pressure |
+| 1_Torr | torr | 1_Torr = 1/760_atm | non-SI pressure |
 | 1_mmHg | millimetres of mercury (at 0°C) | 1_mmHg = 13595.1_kg/m%%^%%3*mm*ga | non-SI pressure |
 | 1_inHg | inches of mercury (at 0°C) | 1_inHg = 13595.1_kg/m%%^%%3*in*ga | non-SI pressure |
@@ Line 217: / Line 246: @@
 | **Temperature** ||||
 | Unit | Unit name | Definition | Description |
-| 1_°C | celsius (or degree celsius) | 1_°C Zero: 0_°C → 273.15_K | Base SI temperature (rel. scale) |
+| 1_°C | celsius (or degree Celsius) | 1_°C Zero: 0_°C → 273.15_K | Base SI temperature (rel. scale) |
 | 1_Δ°C | celsius temperature change | 1_Δ°C = 1_ΔK | Change of temperature |
-| 1_°F | farenheit (or degree farenheit) | 1_°F Zero: 0_°F → 459.67_°R | US cust. temp. (rel. scale) |
+| 1_°F | farenheit (or degree Farenheit) | 1_°F Zero: 0_°F → 459.67_°R | US cust. temp. (rel. scale) |
 | 1_Δ°F | farenheit temperature change | 1_Δ°F = 1_Δ°R | Change of temperature |
 | 1_K | kelvin | 1_K | Base SI temperature (abs. scale) |
@@ Line 236: / Line 265: @@
 | 1_Fdy | faraday | 1_Fdy = 96485.33289_C | non-SI electrical charge |
 | 1_H | henry | 1_H = 1_Wb/A | SI inductance |
-| 1_mho | mho (Siemens) | 1_mho = 1_S | non-SI conductance |
+| 1_mho | mho | 1_mho = 1_S | non-SI conductance |
 | 1_S | siemens | 1_S = 1_1/Ω | SI conductance |
 | 1_T | tesla | 1_T = 1_Wb/m%%^%%2 | SI magnetic flux density |
@@ Line 269: / Line 298: @@
 | 1_Bq | becquerel | 1_Bq = 1_1/s | SI radiation |
 | 1_Ci | curie | 1_Ci = 3.7E10_Bq | non-SI radiation |
-| 1_R | rontgen | 1_R = 2.58E-4_C/kg | non-SI radiation |
+| 1_R | roentgen | 1_R = 2.58E-4_C/kg | non-SI radiation |
 | **Viscosity** ||||