I have found a rather simple way to teach significant digits.
Measurement is the process of taking a standard and using it multiple
times to COMPARE it to an object of unknown size. I take a stick one
meter long (the length is immaterial as anything can be defined as a
standard) with no marks on it and define it as a meter. I then measure
the length of the board in front of the classroom by COUNTING how many
times it takes to move the stick end to end to get to the other side of
the board. Of course, it does not come out even so we menatlly divide
the stick into 10 (or however many we wish) equal pieces and estimate
how many of these decimeters it takes to reach the end of the board. Let
us say 6 decimeters. If we counted 4 meters and 6 decimeters, the board
is 4.6 meters long plus or minus 1 decimeter. The digit(s) we obtained
by COUNTING, meters (4) plus one estimated digit (the 6 decimeters) are
all
significant. All COUNTED and one ESTIMATED digit are significant.
Next I take a stick 1 decimeter long with no markings on it and
start
to measure the board by starting at one side and moving the stick end
over end while COUNTING how many times it takes to get to the other
side. Again it does not come out even so I mentally break the decimeter
into 10 equal pieces and estimate how many of these pieces are needed to
reach the end of the board. Let us say 3 (centimeters). Of course, I
will have counted about 46 times I moved the stick so the length of the
board is 46 decimeters plus the 3 centimeters. The length of the board
is 46.3 decimeters plus or minus 1 centimeter. Again, all the digits
obtained from COUNTING plus one ESTIMATED digit are significant.
There might be an advantage to use a completely fictious unit
for this
exercise so the student does not have any preconcieved notions about
what is happening. One could then get a stick 1 centimeter long with no
markings and repeat this process getting about 463 centimeters plus say
7 tenths of a centimeter (millimeter) plus or minus 1 millimeter. Now we
have 4 sig figs. This process also shows nicely why a smaller unit gives
a measurement with less error.