SI Units and Prefixes
Why SI units?
It provides a standard measurement system because there are too many measurement systems around the world which would create confusion.
Prefixes are very useful in expressing physical quantities that are either very large or very small.
For example, we prefer to estimate the area of Singapore as 716.1 km^2 instead of 716100000 m^2.
Order of Magnitude
To appreciate what you will see at different order of magnitude, you might want to watch the video below.
For simple unit conversion, you can simply multiply or divide by the appropriate power of the ten found in the above table.
4567.8 km = 4567.8 * 103 m = 4567800 m
4567.8 cm = 4567.8 * 10-2 m = 4567.8 * 10-2 ÷ 103 = 0.045678 km
Another method of unit conversion can be found here.
For derived unit conversion, you have to do the following conversion step by step:
(i) 123.4 km/h = ? m/s
123.4 km/h = (123.4*103 m)⁄(3600 s) = 34.3 m/s
Step: convert 123.4 km to 123.4 * 103 m on numerator and 1 h to 3600 s on denominator.
(ii) 345.6 g/cm3 = ? kg/m3
345.6 g/cm3 = (345.6*10-3 kg)⁄((10-2)3 m3) = 345600 kg/m3
Step: convert 345.6 g to 345.6 * 10-3 kg on numerator and 1 cm3 = (10-2)3 m3 (as 1 cm = 10-2 m) on denominator.