All systems have something in common: they measure the same physical quantities, but the standard
“amount” may vary from system to system.
Because different units of distance still measure
you can easily convert from one system to another if you know the
rate”) between systems.
Consider a conversion of 1 ft to cm knowing 1 in = 2.54 cm
In the conversion above, begin with the amount needing conversion.
Because we don’t know the
conversion factor from cm to ft, we will need to use a
conversion to go from ft to in, then inches
Multiply the original value by the conversion factor in a way that makes sense (this means it is
not 1 ft × 1 ft, instead we use 1 ft × 12 inches / ft).
Use the second conversion factor next.
method is a convenient way to keep track of conversions without using a large number of ( ) × ( ) ×
Once all the necessary conversion factors are charted up, cancel units that match on top and bottom.
Multiply across the top and multiply across the bottom.
Simplify the result if it remains a fraction.
More often than not, your conversions will be within the same unit system (from one prefix to another).
Because the decimal system is based in tens, it is very easy to work with because we can simply shift the
decimal point left or right.
For example, convert 34.6 mm to m.
Our intuition tells us to move the
three places to the left
because it’s divided by 1000, for a result of 0.0346 m.
A common mistake students make is to
use this logic on areas, volumes, or anything that’s squared.
example, convert 36 cm
An easy trap to fall into is to move the decimal two places and call it
When the conversion happens for a square, it happens twice: once for the “length” and once for the
This logic applies to any squared quantity, even if “squared
as a unit is hard for us to
Because the math is much more difficult to remember to do mentally, it is a good idea to
do any unit conversions
plugging them into squares.
The same mentality applies to volumes and
raised to a power.