Units

Units are the references we use to measure real world phenomena. They are either defined in relation to real world measurement, or in relation to other units.

1. Quantity 🔗

Units themselves do not carry quantities, nor do quantities carry units. That said, both must be notated for concrete measurements. Twelve is a an abstract quantity, and egg is an abstraction of a physical item. A dozen eggs, on the other hand, is something you can buy at the grocery store.

Quantities are often rounded to an extent. Three decimal points or three digits of precision is usually a good rule of thumb where precision is not required. Excessive precision makes you look like a know-it-all, or a conspiracy theorist.

Examples of notation for the frequency 20,327 Hz:

Notation	Written
Plain	$20,327 Hz$
Prefixed	$20kHz$
Scientific	$2.0327\cdot10^4 Hz$
Engineering	$20.033E3 Hz$

1.1. Prefixes 🔗

Quantities are often specified by common prefixes.

From Wikipedia 🔗 .

Prefix	Symbol	Factor	Power
tera	$T$	$1000000000000$	$10^{12}$
giga	$G$	$1000000000$	$10^{9}$
mega	$M$	$1000000$	$10^{6}$
kilo	$k$	$1000$	$10^{3}$
hecto	$h$	$100$	$10^{2}$
deca	$da$	$10$	$10^{1}$
(none)	(none)	$1$	$10^{0}$
deci	$d$	$0.1$	$10^{-1}$
centi	$c$	$0.01$	$10^{-2}$
milli	$m$	$0.001$	$10^{-3}$
micro	$μ$	$0.000001$	$10^{-6}$
nano	$n$	$0.000000001$	$10^{-9}$
pico	$p$	$0.000000000001$	$10^{-12}$

1.2. Scientific notation 🔗

Scientific notation specifies quantity in the format of $a \cdot 10^n$ for $1 \leq a \leq 10$ and any integer $n$ . The $\cdot10^n$ can be replaced by $En$ , e.g. $48,000 = 4.8\cdot10^4 = 4.8E4$

1.3. Engineering notation. 🔗

Engineering notation is the same as scientific notation, but with exponents only divisible by 3. This makes them align with prefixes and makes verbal communication easier. Re-using the above example, 48,000 would be written as $48*10^3$ or $48E3$ .

2. SI base units 🔗

Most base units have a historical definition grounded in simpler measurements. In modern times, they are put in relation to very specific physical constants in order to increase precision and to account for modern scientific theories.

For more, see Wikipedia: International System of Units 🔗 .

2.1. Time 🔗

Time has the common symbol t.

Unit	Symbol	Defined by
second	$s$	Historically, a division of the day

2.2. Length 🔗

Length has the common symbol l.

Unit	Symbol	Defined by
meter	$m$	Historically, 10,000 km was the distance from the equator to the north pole
inch	$in$ or $"$	$2.54 cm$
foot	$foot$ or $'$	$12 in$
yard	$yd$	$3 feet$
mile	$mi$	$1,760 yd$
Swedish mile	$mil$	$10km$

2.3. Mass 🔗

Mass has the common symbol m. It is commonly referred to as weight, but weight is rather force caused by gravity.

Unit	Symbol	Defined by
gram	$g$	Historically, $1 kg$ is the mass of one liter of water.
pound	$lb$	circa $0.454 kg$
ounce	$oz$	$1/16$ pound
stone	$st$	$14$ pounds

2.4. Temperature 🔗

Temperature has the common symbol T.

Unit	Symbol	Defined by
Kelvin	$K$	The same scale as celsius, but $0K$ , absolute zero, equals $-273.15 \degree C$
Celsius	$\degree C$	Linear scale where $0 \degree C$ is the freezing temperature of water and $100 \degree C$ is the boiling temperature of water
Farenheit	$\degree F$	Exact origins vague, but temperature defined in relation to Celsius as $T_{\degree F} = \dfrac{5}{9}(x − 32) T_{\degree C}$
Rankine	$\degree Ra$	As Kelvin is to Celsius, $T_{°Ra} = \dfrac{5}{9} T_K$

2.5. Current 🔗

Current uses the symbol $I$ .

Unit	Symbol	Defined by
Ampere	$A$	Historically, coloumb per second

The SI definition of ampere was formerly charge over time, with ampere being defined as coloumb per second. Later revisions has reversed the relation, and an ampere is technically defined directly as $6.241509074 \cdot 10^{18} \dfrac{e^-}{s}$ .

3. Unnamed SI derived units 🔗

A few units relatively fundamental to the human experience don't have SI names and are just referred to by their relation to the base units. However, historical named units may exist.