Like scientific notation, unit prefixes make very large and very small numbers easier to manipulate and understand.
Converting numbers from one metric prefix to another is a common task in many areas of science. For example, a lab may stock a 10 gram per liter (g/l) solution of glucose, while a particular procedure may require a 100 μg/l of glucose solution. To perform the procedure, a technician needs to know the concentration** of the stock solution in μg/l.
Converting between metric prefixes is also necessary when the information available to solve a problem is not in the units needed for the answer. This is quite common. For example, if we know that sound travels in air at a speed of 346 m/s, can we figure out how long it will take the sound of an explosion to be heard 1 km away? We can, but to do so, we need to convert between meters and kilometers. The following table shows the relationship between the prefixes.
| Power of 10 |
Prefix |
Symbol |
| 10-18 |
atto |
a |
| 10-15 |
femto |
f |
| 10-12 |
pico |
p |
| 10-9 |
nano |
n |
| 10-6 |
micro |
μ |
| 10-3 |
milli |
m |
| 10-2 |
centi |
c |
| 10-1 |
deci |
d |
| 100 |
(base unit) |
|
| 101 |
deka |
da |
| 102 |
hecto |
h |
| 103 |
kilo |
k |
| 106 |
mega |
M |
| 109 |
giga |
G |
| 1012 |
tera |
T |
| 1015 |
peta |
P |
| 1018 |
exa |
E |
The 103 next to the kilo prefix means that a number with the kilo prefix is 1000 times greater than the same number in the base unit. In the speed of sound question, the 1 km needs to be multiplied by 1000 to convert it to meters (m):
1 km x (1000 m / 1 km ) = 1000 m
Now that the distance is in the same units as speed, we can use the fact that time = distance ÷ speed to calculate the answer:
1000 m / 346 m/s = 2.9 s
The sound of an explosion will be heard 1 km away 2.9 seconds after it happens.
The following illustration explores the relationship between metric prefixes by showing values expressed in different formats and demonstrating the calculations involved in converting numbers from one prefix to the other. Click the "Set/Reset" button to begin or watch the demonstration video below. For practice converting between metric unit prefixes, check out the one step and two step metric prefix conversion problem sets.
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