Units

A unit is an agreed upon size for measuring things. You are probably most familiar with English units, for example feet, gallons, and °F. However, in science, the units used are from within the metric system. Like in the English system where a specific quantity can be measured with different units (a distance can be expressed in feet, inches or miles, for example), the metric system has more than one unit for measuring the same thing. The scientific community has agreed upon which units from the metric system are the official ones for measuring – these are called the SI Units.

Fundamental SI Units

SI units are the internationally agreed upon units used by the scientific community. SI is French for International System.

There are seven fundamental SI units. These are listed in the table below. All physical quantities have units which can be built from these seven base units.

These seven units are called fundamental units because none of them can be expressed as combinations of the other six. This is identical to bricks and concrete being the base units of a building. You can build different things using different combinations of bricks and concrete. The 26 letters of the alphabet are the base units for a language like English. Many different words can be formed by using these letters. A unit built form fundamental units is called a derived unit.

quantity	name	symbol
length	meter	m
mass	kilogram	kg
time	second	s
electric current	ampere	A
temperature	kelvin	K
amount of substance	mole	mol
luminous intensity	candela	cd

The most common SI units

Below are some of the physical quantities you will encounter frequently in physics class, as well as some useful information for converting them to other units.

LENGTH	VOLUME	MASS
SI Unit Meter (m)	SI Unit Cubic Meters (m3)	SI Unit kilogram (kg)
Other common metric units Centimeter (cm): 100cm = 1m	Other common metric units Liter (L): 1000L = 1m3 milliliter (mL): 106mL = 1L	Other common metric units gram (g): 1000g = 1kg Metric ton: (ton): 1ton = 1000kg
English Units Inch (in): 1in = 2.54cm Mile (mi): 1mi = 1609m	English Units Gallon (gal):1gal=3.785L  Quart (qt): 1qt = 946mL	English Units Pounds (lbs): 2.20lbs = 1kg
SPEED	FORCE	TEMPERATURE
SI Unit meters per second (m/s)	SI Unit Newtons (N)	SI Unit Kelvin (K)
Other common metric units Kilometers/hour (kph):1m/s=3.6kph	Other common metric units -	Other common metric units Degrees Celsius (°C): °C = K - 273
English Units Miles/hour (mph): 2.237mph=1m/s	English Units Pounds (lbs): 1lb = 4.448N	English Units Degrees Fahrenheit (°F): °F = (9/5)°C + 32
POWER	ENERGY	PRESSURE
SI Unit Watt (W)	SI Unit Joules (J)	SI Unit Pascal (Pa)
Other common metric units kiloWatt (kW): 1000W = 1kW	Other common metric units electronVolt (eV): 1eV=1.6×10-19J Kilowatt-hour(kWh): kWh=3.6×106J	Other common metric units -
English Units Horsepower (hp): 1hp = 746W	English Units Calorie (kcal): 1kcal = 4190J	English Units Pounds per square inch. (psi): 1psi = 6934Pa Atmosphere (atm): 1atm = 1.013×105Pa

The Metric Prefixes

The table below contains the most common metric prefixes used in the SI system. These should be memorized.

Prefix	Symbol	Exponent	Numerical value
Giga	G	109	1 000 000 000
Mega	M	106	1 000 000
kilo	k	103	1 000
hecto	h	102	100
deca	da	101	10
Base unit		100	1
deci	d	10-1	0.1
centi	c	10-2	0.01
milli	m	10-3	0.001
micro	µ	10-6	0.000 001
nano	n	10-9	0.000 000 001

The metric prefixes are used to convert very large or small numbers into more manageable ones. Because the metric system is based on the number 10, conversion between units is as simple as moving the decimal point to the left or right.

rules for converting between metric prefixes

• To convert to a larger prefix, move the decimal point to the left 1 place for each power of 10 you want to change.
• To convert to a smaller prefix, move the decimal point to the right 1 place for each power of 10 you want to change.

Examples

The distance to the moon is 384,000,000m (384 million meters). The decimal point can be moved 6 places (Mega=10⁶) to the left. The prefix Mega means million so we express the number instead as 384Mm (384 Megameters).

The diameter of an atom is about 0.0000000005m (0.5 billionths of a meter). The decimal point can be moved 9 places (nano=10^-9) to the right. The prefix nano means billionth, so we express the number instead as 0.5nm (0.5 nanometers).

Here are some other examples of the use of prefixes:

• 40,000m can be written as 40km (kilometer)
• 0.001g is the same as 1×10⁻³g and can be written as 1mg (milligram)
• 2.5×10⁶ N can be written as 2.5MN (MegaNewton)
• 250,000A can be written as 250kA (kiloAmpere) or 0.250MA (MegaAmpere)
• 0.000000075s can be written as 75ns (nanoseconds)
• 3×10⁻⁷mol can be rewritten as 0.3×10⁻⁶mol, which is the same as 0.3μmol (micromol)

Familiarity with the Most Common Metric Units

What is your mass in kilograms? Is 150mL of acid a lot? What is your height in centimeters? Is 45°C hot? You should be able to describe common experiences using metric units. Use the table below to become familiar with the most common metric units.

Metric Unit	Closest English Equivalent	Conversion Factor	Common Example
meter	yard	1 m = 3.28 feet	A table is about 1 meter high
centimeter	inch	2.54 cm = 1 in	Your pinky finger is about 1 cm thick.
kilogram	pound	1 kg = 2.2 lbs	An average high school students has a mass of 65 kg (143 lbs)
liter	quart	1 L = 1.06 qt	2-liter bottle of Coca-Cola
milliliter (same as a cubic centimeter)	teaspoon	4.93 mL = 1 tsp	A can of Coke is 330 mL
Celsius	Fahrenheit	°C=5/9(°F-32)	Water freezes at 0°C and boils at 100°C

Converting between units

It is easy to convert between units if the conversion factor is known. Follow the examples below.

• Question
• A
• B
• C