Fully worked out and explained unit conversion problem: Tornados can have huge wind speeds. An F4 tornado (not
even the biggest tornado) can have a wind speed listed as 250 mi/h. The metric units for speed in the SI (metric system
is m/s). What is the wind speed of the tornado in m/s?
Follow the steps to solve the problem.
1) Look what units you have currently, and what units you want to end with.
 250 mi/h to m/s in the example
2) Treat different types of conversions separately
 We have a distance and a time conversion, so you'd have 250 mi  m and 1 h  s (it’s 1 h because 250 mi/h
is 250 mi every 1 h)
3) Using the given conversion factors and KHDBDCM make a plan how to get from current units to desired units.
Remember, there are almost always multiple CORRECT ways to get to the answer.
 For the distance conversion:
o There is only one conversion listed using miles: mi  ft, so we have to convert mi  ft first.
o From ft we have 3 choices: ft  miles (which would undo the work we just did so isn’t a good
option), ft  in, or ft  cm. Since our end goal is m, we want to go to something that can be
ultimately changed to m, both inches and cm will get us there (inches can be converted to cm and
cm is a decimal shift to convert to m). So, I’ll choose the more direct route, ft  cm
o There are no m listed in the given conversions, but we’ve gotten to cm (and since both cm and m
have meters as the base unit, we can use KHDBDCM to do cm  m)
o So my overall plan for the distance conversion will be mi  ft  cm  m
 For the time conversion:
o There is a direct conversion between hours and seconds listed.
o So my overall plan for the time conversion will be h  s
4) Make a grid with as many columns as items in the plan (excluding any that can be one with KHDBDCM)
 Distance: 3 columns (4 items in plan but one is done with KHDBDCM) – 1 for the mi over 1, the next for the
mi  ft conversion, and the last for the ft  cm conversion (the cm  m is just moving the decimal point so
doesn't need a grid). Time: 2 columns – 1 for the h over 1, and one for the h s conversion.
 Always start the first column with the original (or decimal shifted) value as a fraction over 1 (if the first
conversion is a KHDBDCM conversion, use the decimal shifted number as the first grid)
o The example of 250 mi/h does not have a metric-to-like-base-metric conversion to start. So, let’s
assume you had a different problem to help illustrate the decimal shifted case:
 If the first conversion was 51.2 m to cm, we'd shift the decimal 2 places to the right B  C
(base unit to centi-) in KHDBDCM and get 5,120 cm so the first grid would be:
orig value
5,120 cm
1
 The first column of our actual 250 mi/h example would be:
orig value
250 mi
1
 Then each additional column has the next conversion such that unwanted units will cancel out (unwanted
units must be in the numerator of one column and denominator of another column to cancel out). It is
VERY important that each conversion factor used shows physically equal measurements (like 1 ft = 12 in, 1
ft and 12 in are physically the same length, likewise 60s = 1 min, 60s and 1 min are physically the same
length of time)
o
Since mi ft is our next conversion, 1 mi = 5280 ft, since mi is on the numerator of the first grid,
we’d have to put mi on the denominator of the 2nd grid and ft on the numerator of the 2nd grid.
Notice the mi cancel, because they are the same unit. Note however,
orig value
that the numbers do not cancel, because 250 and 1 are not the same
250 mi
5280 ft
values (only the same values/units in numerator and denominator can
1
1 mi
cancel).
o The full distance conversion for the 250 mi  m conversion would be:
orig value mi  ft ft  cm
For cm  m, take answer and use KHDBDCM and shift
250 mi
5280 ft 30.48 cm
decimal 2 places to the left (C  B)
1
1 mi
1 ft
o
We do the same for the h  s conversion
orig value h  s
1h
3600 s
1
1h
5) Calculate using the grid by multiplying all top numbers and dividing by all bottom numbers.
 In the case of my example, for the distance, we'd have 250 x 5280 x 30.48 ÷ 1 ÷ 1 ÷ 1 (but we don't have to
actually do the divides by 1 because that won't change the answer).
o Plugging this into a calculator and we get 40233600 cm (decimal would be after last zero in unshifted number), but we need it in m, so in KHDBDCM, you have to go 2 places to the left to get from
c to b (meters are the base units), so our distance would be 402336.00 m. Make sure NOT TO
ROUND UNTIL PROBLEM IS DONE
 In the case of the time we’d get 1 · 3,600 ÷ 1 ÷ 1, but dividing/multiplying by 1 doesn’t change the answer,
so we get the time is 3600 s
 So at this point we know the distance is 402336.00 m and the time is 3600 s
6) If there are two different conversions, do the final operation shown by the units.
 Since we're trying to get m/s, we need to divide our m answer by our s answer.
 Unrounded answer is: 402336.00 / 3600 = 111.76 m/s.
 Now we need to round to the correct number of significant figures, so we have to look at all the numbers
used in the calculations. Remember all of the numbers combine to come out as a group, so we have to look
for the “slowest runner” (least significant figures) and that will dictate the “maximum speed” (most precise,
or most number of significant figures, we can express) for the answer.
o All of the conversions used were exact measurements (no estimation or rounding done), so they
don’t affect the reliability of the overall answer (for example, we could have written 1 ft = 30.48 cm
as 1.0000000 ft = 30.480000000 cm, because we know they are exact, so they can have as many
significant figures as we need – they are the Usain Bolts of the calculation and can keep up with any
measurement so exact numbers don’t slow down the group (the answer) at all.
o The original number, 250, only has 2 significant figures; the trailing zero doesn’t count since there is
no decimal point shown. So the 2 significant figures is the “slowest runner” of the numbers and we
need to round our answer to 2 significant figures.
o The 111.76 will round after the 2nd 1, so the 10s digit will round down to 1 (the 1 in the ones digit isn’t
halfway to the 10 yet), so we’ll have 110 (notice we still need a place holder for the ones place even
though we rounded it off, we couldn’t say 11 ≈ 111.76, but we certainly can say 110 ≈ 111.76
o Notice we also cannot add decimal point (as in 110. or 110.0) because with the decimal point shown,
trailing zeroes are significant – that would say there are 3 or 4 significant figures respectively.
 So for our final answer, 111.76 m/s rounds to 110 m/s (or 1.1x102 m/s in sci. not.) to 2 significant figures