1.1 Use of SI Units and their prefixes
Fundamental units
Fundamental units are the units from which every other unit can be derived from.
Quantity Unit Name
Mass kg kilogram
Length m metre
Time s second
Amount of substance mol mole
Temperature K kelvin
Electric current A amperes (amps)
SI Prefixes
A prefix indicates that the quantity is a multiple or fraction of the base unit. For example, 2
km is 2,000 m.
Prefix
T
G
Name
tera
giga
CONB007 Proportion of base unit
1, 000, 000, 000, 000
1, 000, 000, 000( )
( )
10
9
10
12
M mega ( )
1, 000, 000 10
6
k kilo ( )
1, 000 10
3
c centi 1/100( )
10
−2
m milli (
1/1, 000 10 ) −3
μ micro (
1/1, 000, 000 ) 10
−6
n nano (
1/1, 000, 000, 000 ) 10
−9
p pico (
1/1, 000, 000, 000, 000 ) 10
−12
f femto (
1/1, 000, 000, 000, 000, 000 10
−15
)
To convert from a prefixed unit into the base unit, multiply by the proportion.
Example
5 ms = 5 × 10
−3
s = 0.005 s
To convert from a base unit into a prefixed unit, divide by the proportion.
Example
, 7, 500 m = 7, 500 ÷ 10
3
km = 7.5 km
Tip
It can make converting easier if you replace the prefix with the word. For example, read 3 kA
as "3 thousand amps"
Caution
The fundamental unit of mass is the kilogram, not the gram! For example, if you were to
convert 3 mg into base units, convert to g first then convert to kg.
Derived units
Units that are not fundamental units are called derived units. For example, Hz is a derived
unit.
To turn a derived unit back into base units, you need to use formulae that contain the unit
you must derive.
If a unit has "per" in it, like how speed is "metres per second", a negative exponent will be
used. (e.g. m/s becomes m s⁻¹)
Example CONB007
To derive the units for N, you can use the f orce = mass × acceleration
Replace each quantity with its unit:
−2
N = kg × m s
This means N in base units is kg m s⁻².
Units of the same quantity
J and eV (electron volt) are both quantities for energy, but they are different sizes:
−19
1 eV = 1.60 × 10 J
The value 1.60 × 10 is and is on the datasheet
−19
e
To convert from eV to J, multiply by . To convert from J to eV, divide by .
e e
kW h is also a unit for energy and we can convert to J by doing the following:
Use power =
energy
time
kW h -> kJ s⁻¹ h
Convert hours into seconds
kJ s⁻¹ h -> kJ s⁻¹ 3,600 s
Cancel out s and s⁻¹
kJ s⁻¹ 3,600 s -> kJ 3,600
Fundamental units
Fundamental units are the units from which every other unit can be derived from.
Quantity Unit Name
Mass kg kilogram
Length m metre
Time s second
Amount of substance mol mole
Temperature K kelvin
Electric current A amperes (amps)
SI Prefixes
A prefix indicates that the quantity is a multiple or fraction of the base unit. For example, 2
km is 2,000 m.
Prefix
T
G
Name
tera
giga
CONB007 Proportion of base unit
1, 000, 000, 000, 000
1, 000, 000, 000( )
( )
10
9
10
12
M mega ( )
1, 000, 000 10
6
k kilo ( )
1, 000 10
3
c centi 1/100( )
10
−2
m milli (
1/1, 000 10 ) −3
μ micro (
1/1, 000, 000 ) 10
−6
n nano (
1/1, 000, 000, 000 ) 10
−9
p pico (
1/1, 000, 000, 000, 000 ) 10
−12
f femto (
1/1, 000, 000, 000, 000, 000 10
−15
)
To convert from a prefixed unit into the base unit, multiply by the proportion.
Example
5 ms = 5 × 10
−3
s = 0.005 s
To convert from a base unit into a prefixed unit, divide by the proportion.
Example
, 7, 500 m = 7, 500 ÷ 10
3
km = 7.5 km
Tip
It can make converting easier if you replace the prefix with the word. For example, read 3 kA
as "3 thousand amps"
Caution
The fundamental unit of mass is the kilogram, not the gram! For example, if you were to
convert 3 mg into base units, convert to g first then convert to kg.
Derived units
Units that are not fundamental units are called derived units. For example, Hz is a derived
unit.
To turn a derived unit back into base units, you need to use formulae that contain the unit
you must derive.
If a unit has "per" in it, like how speed is "metres per second", a negative exponent will be
used. (e.g. m/s becomes m s⁻¹)
Example CONB007
To derive the units for N, you can use the f orce = mass × acceleration
Replace each quantity with its unit:
−2
N = kg × m s
This means N in base units is kg m s⁻².
Units of the same quantity
J and eV (electron volt) are both quantities for energy, but they are different sizes:
−19
1 eV = 1.60 × 10 J
The value 1.60 × 10 is and is on the datasheet
−19
e
To convert from eV to J, multiply by . To convert from J to eV, divide by .
e e
kW h is also a unit for energy and we can convert to J by doing the following:
Use power =
energy
time
kW h -> kJ s⁻¹ h
Convert hours into seconds
kJ s⁻¹ h -> kJ s⁻¹ 3,600 s
Cancel out s and s⁻¹
kJ s⁻¹ 3,600 s -> kJ 3,600
