Units & Prefixes

Base Units

The SI system of units has 7 base units, from which all other units are derived:

Quantity	Unit	abbreviation	Defining Physical Constant
length	metre	$m$	speed light in vacuo, $c$
mass	kilogram	$kg$	planck's constant, $h$
time	second	$s$	caesium standard, $Δ v_{Cs}$
temperature	kelvin	$K$	boltzmann constant, $k_{B}$
electrical current	ampere	$A$	fundamental charge, $e$
amount of a substance	mole	mol	avogradro's constant, $N_{A}$
luminous intensity	candela	cd	k_cd

Note: Luminous intensity is not generally covered at GCSE or A level.

Prefix		Base 10	Decimal	English word
Name	Symbol	Base 10	Decimal	Short scale	Long scale
quetta	Q	$10^{30}$	1 000 000 000 000 000 000 000 000 000 000	nonillion	quintillion
ronna	R	$10^{27}$	1 000 000 000 000 000 000 000 000 000	octillion	quadrilliard
yotta	Y	$10^{24}$	1 000 000 000 000 000 000 000 000	septillion	quadrillion
zetta	Z	10²¹	1 000 000 000 000 000 000 000	sextillion	trilliard
exa	E	10¹⁸	1 000 000 000 000 000 000	quintillion	trillion
peta	P	10¹⁵	1 000 000 000 000 000	quadrillion	billiard
tera	T	10¹²	1 000 000 000 000	trillion	billion
giga	G	10⁹	1 000 000 000	billion	milliard
mega	M	10⁶	1 000 000	million
kilo	k	10³	1 000	thousand
hecto	h	10²	100	hundred
deca	da	10¹	10	ten
		10⁰	1	one
deci	d	10^-1	0.1	tenth
centi	c	10^-2	0.01	hundredth
milli	m	10^-3	0.001	thousandth
micro	µ	10^-6	0.000 001	millionth
nano	n	10^-9	0.000 000 001	billionth	milliardth
pico	p	10^-12	0.000 000 000 001	trillionth	billionth
femto	f	10^-15	0.000 000 000 000 001	quadrillionth	billiardth
atto	a	10^-18	0.000 000 000 000 000 001	quintillionth	trillionth
zepto	z	10^-21	0.000 000 000 000 000 000 001	sextillionth	trilliardth
yocto	y	10^-24	0.000 000 000 000 000 000 000 001	septillionth	quadrillionth
ronto	r	10^-27	0.000 000 000 000 000 000 000 000 001	octillionth	quadrilliardth
quecto	q	10^-30	0.000 000 000 000 000 000 000 000 000 001	nonillionth	quintillionth

All the prefixes are listed here, but only those between tera and femto are needed for GCSE and A level.

Most units of measure out side SI are called customary or imperial measures. Here are some you need to know.

Distance (long): 1 mile = 1.6 kilometres; 0.62 miles = 1 kilometre; 5 miles = 8 kilometres
Distance (short): 1 inch = 2.5 centimetres; 0.39 inches = 1 centimetres; 2 inches = 5 centimetres
Mass: 2.2 pound = 1 kilograms; 1 pound = 0.45 kilograms; 11 pounds = 5 kilograms/
Volume: 1 gallon = 4.5 litres; 0.22 gallons = 1 litre; 2 gallons = 9 litres

Metric units (length) Video: Practice Questions; Textbook Exercise
Metric units (mass) Video: Practice Questions; Textbook Exercise
Metric units (capacity) Video: Practice Questions; Textbook Exercise
Metric to imperial (length) Video: Practice Questions
Metric to imperial (mass) Video: Practice Questions
Metric to imperial (capacity) Video: Practice Questions
Conversion graphs (draw) Video: Practice Questions; Textbook Exercise
Conversion graphs (interpret) Video: Practice Questions; Textbook Exercise
Converting imperial units for length Video: Practice Questions
Converting imperial units for mass Video: Practice Questions
Converting imperial units for capacity Video: Practice Questions; (Care of corbettmaths.com)

Name	Symbol	Quantity	Value in SI units
astronomical unit	$au$	length	$1.495 \times 10^{11} m$
light-Year	$ly$		$9.461 \times 10^{15} m$
Parsec	$p c$		$3.086 \times 10^{16} m$
tonne	$t$	mass	$1 M g = 1000 k g$
dalton	Da	mass	$1 D a = 1.661 \times 10^{−27} k g$
minute	min	time	1 min = 60 s
hour	h		1 h = 60 min = 3,600 s
day	d		1 d = 24 h = 1,440 min = 86,400 s
degree	°	plane angle and phase angle (waves)	1° = π/180 rad
arcminute	′		1′ = 1/60° = π/10,800 rad
arcsecond	″		$1^{″} = {(\frac{1}{60})}^{'} = {(\frac{1}{3600})}^{°} = (\frac{π}{648000}) rad$
hectare	$ha$	area	$1 h m^{2} = 10,000 m^{2}$
litre	l, L	volume	$1 L = 1 d m^{3} = 1000 c m^{3} =0.001m^{3}$
electronvolt	$e V$	energy	$1 e V = 1.602 \times 10^{-19} J$