Multiple and Sub-Multiple Units
 Imagine you are to run a marathon race. Would it not be easier to visualize a distance of 30
kilometers rather than 30 000 meters? Units, such as the kilometer, which are larger than the
fundamental unit, in this case, meter, are called multiple units.
 Now imagine measuring the diameter of a coin. Which would you prefer to say: 5 millimeters
or 0.005 meters? You would agree that 5mm is more practical. Units, such as the millimeter,
which are smaller than the fundamental unit, are called sub-multiple units.
There are several multiple and sub-multiple units which are larger or smaller than the fundamental
quantity and are written in terms of powers of 10 with each having a designated prefix.
PREFIX SYMBOL VALUE
PREFIX SYMBOL VALUE
Kilo
𝑘�
103
milli
𝑚�
Mega
𝑀�
106
micro
𝜇�
Giga
𝐺�
109
nano
𝑛�
Tera
𝑇�
1012
Figure 1.3 Multiples and their value
10−3 or
10−9or
1
1000000000
pico
𝑝�
10−12or
1
1000000000000
Figure 1.4: Sub-multiples and their value N.B.
The value listed is how much times bigger or smaller the prefix is than the base unit.
Converting from the Multiple or Sub-Multiple Unit to the base unit:
When converting from multiple or sub-multiple units to the base unit, simply multiply the number
to be converted by the value of the multiple or sub-multiple prefixes
pg. 1
EXAMPLE 2: Convert 36000 𝜇 m to m
���
micro = 10−6 or 1
1000000
Thus, multiply 36000 by
𝟏
𝟏�𝟎�𝟎�𝟎�𝟎�𝟎�𝟎
1
36000μm = (36000×
)m
1000000
= 0.036m
ANS: 0.036 metres
N.B Multiplying by
1
1000000
is = dividing by 1000000
EXAMPLE 1:
Convert 1500km to m
kilo = 103or 1000
Thus, multiply 1500 by 𝟏�𝟎�𝟑� or 1000.
1500km = (1500 × 1000)m
= 1 500 000 m
ANS: 1 500 000 metres
pg. 2