Scales ------ | Scale | meaning | C or D= | length (L) | |-------|------------------|----------------|----------------| | C/D | C | C | log(C) | | A/B | C^2 | sqrt(A) | log(A)/2 | | K | C^3 | cbrt(K) | log(K)/3 | | CI | 1/C | 1/CI | -log(CI) | | L | log(C) | 10^L | L | | LL1 | e^(C/100) | ln(LL1)*100 | 1+log(ln(LL1)) | | LL2 | e^(C/10) | ln(LL2)*10 | 2+log(ln(LL2)) | | LL3 | e^C | ln(LL3) | log(ln(LL3)) | | T | arctan(C) | tan(T) | log(tan(T)) | | S | arcsin(C) | sin(S) | log(sin(S)) | | ST | inv arclen(C) | sin=tan=arclen | log(arclen | | P | sqrt(1-(C/10)^2) | sqrt(1-P^2)*10 | 1+log(1-P^2)/2 | | xxF | Folded | shifted(xx) | xx + 0.5 | Settings -------- ``` a = b*c or b = a/c --------------------- C | 1 c | --------------------------- D | b a | --------------------- ``` ``` a/b = c/d = e/f... --------------------- C | a c e | --------------------------- D | b d f | --------------------- ``` ``` a = b^c --------------------- C | 1 c | --------------------------- LL | b a | --------------------- ``` ``` a = b*c*d a = b/c/d a = b*c/d ``` ``` --------------------- | | --------------------------- | | --------------------- ``` ``` --------------------- | | --------------------------- | | --------------------- ``` ``` A /| / | c/ |b / | / | B-----C a ``` ``` A /\ / \ c/ \b / \ / \ B----------C a --------------------- C | a b c | --------------------------- S | A B C | --------------------- ``` Ratios ------ The numerical values adopted by the CGPM[36] are identical to the published CODATA 2017 values.[37] Following the successful 1983 redefinition of the metre in terms of an exact numerical value for the speed of light, the BIPM's Consultative Committee for Units (CCU) recommended and the BIPM proposed that four further constants of nature should be defined to have exact values. These are:[Note 5] The Planck constant h is exactly 6.62607015e−34 joule-second (J⋅s). The elementary charge e is exactly 1.602176634e−19 coulomb (C). The Boltzmann constant k is exactly 1.380649e−23 joule per kelvin (J⋅K−1). The Avogadro constant NA is exactly 6.02214076e23 reciprocal mole (mol−1). The redefinition retains unchanged the numerical values associated with the following constants of nature: The speed of light c is exactly 299792458 metres per second (m⋅s−1); The ground state hyperfine structure transition frequency of the caesium-133 atom ΔνCs is exactly 9192631770 hertz (Hz); The luminous efficacy of monochromatic radiation of frequency 5.40×1014 Hz (540 THz) – a frequency of green-colored light at approximately the peak sensitivity of the human eye – Kcd (where the subscript "cd" is the symbol for candela) is exactly 683 lumens per watt (lm⋅W−1). The seven SI defining constants above, expressed in terms of derived units (joule, coulomb, hertz, lumen, and watt), are rewritten below in terms of the seven base units (second, metre, kilogram, ampere, kelvin, mole, and candela);[4] the dimensionless unit steradian (symbol sr) is also used: ΔνCs = Δν(133Cs)hfs = 9192631770 s−1 c = 299792458 m⋅s−1 h = 6.62607015e−34 kg⋅m2⋅s−1 e = 1.602176634e−19 A⋅s k = 1.380649e−23 kg⋅m2⋅K−1⋅s−2 NA = 6.02214076e23 mol−1 Kcd = 683 cd⋅sr⋅s3⋅kg−1⋅m−2 As part of the redefinition, the International Prototype of the Kilogram was retired and definitions of the kilogram, the ampere, and the kelvin were replaced. The definition of the mole was revised. These changes have the effect of redefining the SI base units, though the definitions of the SI derived units in terms of the base units remain the same. ### Counting 1728 units = 144 dozen = 12 gross = 1 great gross 20 units = 1 score 1 mol = N(A) = 6.02214076e23 ~ 1090/181e23 #### Metric/SI/IEC/JEDEC | Prefix | Symbol | Factor | Number Name | |------------|--------|------------------ |----------------| | quecto | q | 10^-30 = 1000^-10 | nonillionth | | ronto | r | 10^-27 = 1000^-9 | octillionth | | yocto | y | 10^-24 = 1000^-8 | septillionth | | zepto | z | 10^-21 = 1000^-7 | sextillionth | | atto | a | 10^-18 = 1000^-6 | quintillionth | | femto | f | 10^-15 = 1000^-5 | quadrillionth | | pico | p | 10^-12 = 1000^-4 | trillionth | | nano | n | 10^-9 = 1000^-3 | billionth | | micro | μ | 10^-6 = 1000^-2 | millionth | | milli | m | 10^-3 = 1000^-1 | thousandth | | centi | c | 10^-2 | hundredth | | deci | d | 10^-1 | tenth | | - | - | 10^0 = 1000^0 | one/unit/whole | | deka | da | 10^1 | ten | | hecto | h | 10^2 | hundred | | kilo | k | 10^3 = 1000^1 | thousand | | kibi/kilo | Ki/K | 2^10 = 1024^1 | - | | mega | M | 10^6 = 1000^2 | million | | mebi/mega | Mi/M | 2^20 = 1024^2 | - | | giga | G | 10^9 = 1000^3 | billion | | gibi/giga | Gi/G | 2^30 = 1024^3 | - | | tera | T | 10^12 = 1000^4 | trillion | | tebi/tera | Ti/T | 2^40 = 1024^4 | - | | peta | P | 10^15 = 1000^5 | quadrillion | | pebi | Pi | 2^50 = 1024^5 | - | | exa | E | 10^18 = 1000^6 | quintillion | | exbi | Ei | 2^60 = 1024^6 | - | | zetta | Z | 10^21 = 1000^7 | sextillion | | zebi | Zi | 2^70 = 1024^7 | - | | yotta | Y | 10^24 = 1000^8 | septillion | | yobi | Yi | 2^80 = 1024^8 | - | | ronna | R | 10^27 = 1000^9 | octillion | | quetta | Q | 10^30 = 1000^10 | nonillion | ### Time 1 day = 24 hours = 1440 minutes = 86400 seconds 400 Gregorian years = 146097 days = 20871 weeks = 4800 months = 4 centuries = 0.4 millennia 4 Julian years = 1461 days = 48 months 1 lunar sidereal month ~ 27.32 days 1 lunar synodic phase month ~ 29.53 days 1 solar year ~ 365.2422 days Hertz = cycles/second ~ radians/sec ~ degrees/sec ### Geometry and Mathematics pi = 710/226 tau = 1420/226 = 710/113 e = 685/252 phi = 466/288 180 degrees = pi radians = 200 grads = 0.5 turns 2120 degrees ~ 37 radians ### Physical G = gravitation = 6.674e-11 = 494/74e-11 m^3/(kg s^2) h = Plank = 6.62607015e-34 = 815/123 = 1630/246e-34 (J s) k = Boltzmann = 1.380649e-23 = 214/155e-23 J/K fine structure constant = 7.297e-3 = 270/37e-3 ~ 1/137 E0 = vacuum permittivity = 8.854e-12 = 850/96e-12 F/m μ0 = vacuum permeability = 4*pi e-7 H/m = 1.2566e-6 = 142/113e-6 N/A^2 F = Faraday constant = 9.6485e4 = 1920/199e4 C/mol ΔνCs = Δν(133Cs)hfs = 9192631770 s−1 Kcd = 683 cd⋅sr⋅s3⋅kg−1⋅m−2 ### Temperature absolute zero = -273.15 C = 0 K = -495.69 F = 0 R triple point of water = 0.01 C = 273.16 K = 32.018 F = 527.708 R boiling water @ 1 atm = 100 C = 373.15 K = 212 F = 707.69 R F C K R ### Mass pound kilo ton atomic mass unit ~ 1.66e-27 ounces metric ton gram kilogram megagram ### Distance 5 inches = 127 mm 12 inches = 1 feet inches meter foot mile nautical mile yard angstrom ### Area sq inches sq meter sq cm sq foot sq mile yard acre hectare ### Volume cb inches cb meter cb cm cb foot cb mile cb yard pint mL liter quart gallon cups tablespoon teaspoon oz barrels(oil) acre feet ### Pressure 1 atm pounds/sq inch pascal N/m^2 millibars pounds/sq foot mmHg feetH20 ### Speed light = c = 299792458 m/s ~ 995/332e8 kph mph mps knots ft/min ### Money - **$1 ~1 silver piece ~ 25g silver ~ 1 US silver dollar ~ 1 thaler ~ 1 Spanish dollar ~ 1 silver yen ~ 1 silver yaun ~ 1 silver trade coin** ### Energy electron Volt BTU Joule foot pounds calorie Watt hour ### Light foot candels lux candelas ### Force Newton dynes ### Power Horsepower Watt BTU / hour V A ### Charge electron = 1.602176634e-19 C ~ 149/93e-19 ## New units - turn or cycle - measure of angle - 1 milliturn is 1000 of the way around a circle - yottas - 10^24 units - - charge of a yottas of down quarks - - mass of a yottas of He-4 - approx 6.642156 grams - millinaut or stave - approx 1/1000 of a nautical mile - approx 540 millinauts = 1 km - approx 6.076 feet - 1 inch = 13.716 micronauts - very approx the height of a man - very approx the wing span of a man - ?? approx 532 millinauts = 1 km - - volume - 1 ml = 0.157464 cubic staves - 1 pt - ??1 ml = 0.1505535 cubic stave - temperature - 0 = absolute zero - 1000 = triple point of water - 1366 ~ boiling point of water @ 1atm c = 161887940 staves/sec - second - time it takes light to travel *c* - approx 1/86400 of an earth day