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manual:chapter3:units [2018/10/25 10:09] claudio |
manual:chapter3:units [2019/09/18 16:30] jojo1973 [Multiples and Submultiples] |
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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. \\ | 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. \\ | ||
'' | '' | ||
+ | |||
+ | ==== Multiples and Submultiples ==== | ||
+ | |||
+ | Multiples and submultiples of many units are obtained by prefixing them with the standard SI prefixes. Therefore, '' | ||
+ | |||
+ | 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 '' | ||
+ | |||
+ | ^ SI Prefix | ||
+ | | Y | ||
+ | | Z | ||
+ | | E | ||
+ | | P | ||
+ | | T | ||
+ | | G | ||
+ | | M | ||
+ | | k | ||
+ | | h | ||
+ | | da | $10^{1}$ | ||
+ | | d | ||
+ | | c | ||
+ | | m | ||
+ | | µ | ||
+ | | n | ||
+ | | p | ||
+ | | f | ||
+ | | a | ||
+ | | z | ||
+ | | y | ||
==== Operating with Units ==== | ==== Operating with Units ==== | ||
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Results of an addition or subtraction between consistent units will produce a result with the units of the first argument (argument in level 2 of the stack at the time of the operation, or the left argument in an algebraic expression). | Results of an addition or subtraction between consistent units will produce a result with the units of the first argument (argument in level 2 of the stack at the time of the operation, or the left argument in an algebraic expression). | ||
+ | |||
+ | Unit conversions can be performed directly using the '' | ||
+ | |||
+ | To reduce a unit to its base components, use the command '' | ||
+ | |||
+ | To extract the value part of a unit object, use the '' | ||
==== Custom Units ==== | ==== Custom Units ==== | ||
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| 1_ftUS | surveying foot | 1_ftUS = 1200/3937_m | US surveying length | | | 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_mil | thousandth of inch | 1_mil = 0.001_in | US customary length | | ||
- | | 1_µ | micron | + | | 1_µ | micron | 1_µ = 1_µm | SI length | |
- | | 1_Å | Ångström | + | | 1_Å | ångström |
- | | 1_fermi | fermi or femtometre | + | | 1_fermi | fermi | 1_fermi = 1_fm | SI length | |
| **Area** |||| | | **Area** |||| | ||
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| 1_cu | cup | 1_cu = 1/16_gal | US customary volume | | | 1_cu | cup | 1_cu = 1/16_gal | US customary volume | | ||
| 1_ozfl | fluid ounce | 1_ozfl = 1/128_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_tsp | tea spoon | 1_tsp = 1/6_ozfl | US customary volume | | + | | 1_tsp | teaspoon |
| 1_fbm | board foot | 1_fbm = 144_in%%^%%3 | 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 | | | 1_galUK | gallon (UK) | 1_galUK = 0.00454609_m%%^%%3 | Imperial volume | | ||
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| **Time** |||| | | **Time** |||| | ||
| Unit | Unit name | Definition | Description | | | Unit | Unit name | Definition | Description | | ||
- | | 1_yr | tropical year | 1_yr = 31556925.9747_sper | + | | 1_yr | tropical year | 1_yr = 31556925.9747_s |
| 1_d | day | 1_d = 86400_s | SI time | | | 1_d | day | 1_d = 86400_s | SI time | | ||
| 1_h | hour | 1_h = 3600_s | SI time | | | 1_h | hour | 1_h = 3600_s | SI time | | ||
| 1_min | minute | 1_min = 60_s | SI time | | | 1_min | minute | 1_min = 60_s | SI time | | ||
| 1_s | second | 1_s | Base SI unit of 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** |||| | | **Speed** |||| | ||
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| Unit | Unit name | Definition | Description | | | Unit | Unit name | Definition | Description | | ||
| 1_kg | kilogram | 1_kg | Base SI unit of mass | | | 1_kg | kilogram | 1_kg | Base SI unit of mass | | ||
- | | 1_g | kilogram | + | | 1_g | gram | 1_g = 0.001_kg | SI mass | |
| 1_lb | pound | 1_lb = 7000_grain | US customary mass | | | 1_lb | pound | 1_lb = 7000_grain | US customary mass | | ||
| 1_oz | ounce | 1_oz = 1/16_lb | US customary mass | | | 1_oz | ounce | 1_oz = 1/16_lb | US customary mass | | ||
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| 1_ton | tonne | 1_ton = 2000_lb | US customary mass | | | 1_ton | tonne | 1_ton = 2000_lb | US customary mass | | ||
| 1_tonUK | tonne (UK) | 1_tonUK = 2240_lb | Imperial mass | | | 1_tonUK | tonne (UK) | 1_tonUK = 2240_lb | Imperial mass | | ||
- | | 1_t | Metric | + | | 1_t | metric |
| 1_ozt | troy ounce | 1_ozt = 480_grain | Imperial mass | | | 1_ozt | troy ounce | 1_ozt = 480_grain | Imperial mass | | ||
- | | 1_ct | Metric | + | | 1_ct | metric |
| 1_grain | grain | 1_grain = 64.79891_mg | Imperial 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_u | unified atomic mass | 1_u = 1.660539040E-27_kg | non-SI mass | | ||
| 1_mol | mole | 1_mol | Base SI amount of substance | | | 1_mol | mole | 1_mol | Base SI amount of substance | | ||
| 1_gmol | gram mole | 1_gmol = 1_mol | non-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 |
| **Force** |||| | | **Force** |||| | ||
| Unit | Unit name | Definition | Description | | | Unit | Unit name | Definition | Description | | ||
- | | 1_N | Newton | + | | 1_N | newton |
| 1_dyn | dyne | 1_dyn = 1_g*cm/ | | 1_dyn | dyne | 1_dyn = 1_g*cm/ | ||
| 1_gf | gram-force | 1_gf = 1_g*ga | 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_kip | kip | 1_kip = 1000_lbf | US customary force | | ||
| 1_lbf | pound-force | 1_lbf = 1_lb*ga | US customary force | | | 1_lbf | pound-force | 1_lbf = 1_lb*ga | US customary force | | ||
- | | 1_pdl | poundal | 1_pdl = = 1_lb*ft/ | + | | 1_pdl | poundal | 1_pdl = 1_lb*ft/ |
| **Energy** |||| | | **Energy** |||| | ||
| Unit | Unit name | Definition | Description | | | 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_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_erg | erg | 1_erg = 1_dyn*cm | non-SI energy | | ||
- | | 1_kcal | kilo calorie | + | | 1_kcal | kilocalorie (thermochemical) |
- | | 1_cal | calorie | 1_cal = 4.184_J | non-SI energy | | + | | 1_cal | calorie |
| 1_Btu | british thermal unit | 1_Btu = =1055.056_J | Imperial 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_ft*lbf | foot-pound | 1_ft*lbf = 1_lb*ft*ga | US customary energy | | ||
| 1_therm | therm | 1_therm = 100000_Btu | Imperial energy | | | 1_therm | therm | 1_therm = 100000_Btu | Imperial energy | | ||
- | | 1_MeV | mega electronvolt | + | | 1_MeV | megaelectronvolt |
| 1_eV | electronvolt | 1_eV = 1.6021766208E-19_J | non-SI energy | | | 1_eV | electronvolt | 1_eV = 1.6021766208E-19_J | non-SI energy | | ||
| **Power** |||| | | **Power** |||| | ||
| Unit | Unit name | Definition | Description | | | 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_kW | kilowatt | 1_kW = 1000_W | SI power | | ||
| 1_MW | megawatt | 1_MW = 1000000_W | SI power | | | 1_MW | megawatt | 1_MW = 1000000_W | SI power | | ||
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| **Pressure** |||| | | **Pressure** |||| | ||
| Unit | Unit name | Definition | Description | | | Unit | Unit name | Definition | Description | | ||
- | | 1_Pa | Pascal | + | | 1_Pa | pascal |
| 1_atm | atmospheric pressure | 1_atm = 101325_Pa | non-SI pressure | | | 1_atm | atmospheric pressure | 1_atm = 101325_Pa | non-SI pressure | | ||
| 1_bar | bar | 1_bar = 100000_Pa | non-SI pressure | | | 1_bar | bar | 1_bar = 100000_Pa | non-SI pressure | | ||
| 1_psi | pound per square inch | 1_psi = 1_lbf/ | | 1_psi | pound per square inch | 1_psi = 1_lbf/ | ||
- | | 1_Torr | Torricelli | + | | 1_Torr | torr | 1_Torr = 1/760_atm | non-SI pressure | |
| 1_mmHg | millimetres of mercury (at 0°C) | 1_mmHg = 13595.1_kg/ | | 1_mmHg | millimetres of mercury (at 0°C) | 1_mmHg = 13595.1_kg/ | ||
| 1_inHg | inches of mercury (at 0°C) | 1_inHg = 13595.1_kg/ | | 1_inHg | inches of mercury (at 0°C) | 1_inHg = 13595.1_kg/ | ||
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| **Temperature** |||| | | **Temperature** |||| | ||
| Unit | Unit name | Definition | Description | | | Unit | Unit name | Definition | Description | | ||
- | | 1_°C | celsius (or degree | + | | 1_°C | celsius (or degree |
| 1_Δ°C | celsius temperature change | 1_Δ°C = 1_ΔK | Change of temperature | | | 1_Δ°C | celsius temperature change | 1_Δ°C = 1_ΔK | Change of temperature | | ||
- | | 1_°F | farenheit (or degree | + | | 1_°F | farenheit (or degree |
| 1_Δ°F | farenheit temperature change | 1_Δ°F = 1_Δ°R | Change of temperature | | | 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) | | | 1_K | kelvin | 1_K | Base SI temperature (abs. scale) | | ||
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| 1_Fdy | faraday | 1_Fdy = 96485.33289_C | non-SI electrical charge | | | 1_Fdy | faraday | 1_Fdy = 96485.33289_C | non-SI electrical charge | | ||
| 1_H | henry | 1_H = 1_Wb/A | SI inductance | | | 1_H | henry | 1_H = 1_Wb/A | SI inductance | | ||
- | | 1_mho | mho (Siemens) | + | | 1_mho | mho | 1_mho = 1_S | non-SI conductance | |
| 1_S | siemens | 1_S = 1_1/Ω | SI conductance | | | 1_S | siemens | 1_S = 1_1/Ω | SI conductance | | ||
| 1_T | tesla | 1_T = 1_Wb/ | | 1_T | tesla | 1_T = 1_Wb/ | ||
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| 1_Bq | becquerel | 1_Bq = 1_1/s | SI radiation | | | 1_Bq | becquerel | 1_Bq = 1_1/s | SI radiation | | ||
| 1_Ci | curie | 1_Ci = 3.7E10_Bq | non-SI radiation | | | 1_Ci | curie | 1_Ci = 3.7E10_Bq | non-SI radiation | | ||
- | | 1_R | rontgen | + | | 1_R | roentgen |
| **Viscosity** |||| | | **Viscosity** |||| |