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This video will demonstrate how to perform two difficult conversions:
how to convert a distance from feet and inches to meters,
and how to convert an angle in degrees, minutes and seconds into gradians.
There are two steps an engineer should take when converting composite units,
or readings that are presented in a format with two or more units such as feet and inches.
Because composite units are not presented with typical significant figures -
for example, this distance is given in feet and inches but also includes a fraction of an inch -
the first step involves determining how many significant figures, or sig figs,
should be retained after the conversion. Identify the smallest unit of the number:
here, it is an eighth of an inch. Then, convert the entire measurement to that unit.
The 178 feet must be converted to inches, then converted to eighths of an inch.
This can be accomplished by multiplying by "one" or 8 over 8.
The 6 inches must also be converted into a fraction. Add the three components together.
This conversion reveals the minimum number of significant figures required
to adequately and accurately represent the original number.
The second step in this process is to convert the measurement into the unit of interest;
for this example, meters.
Recall the fraction representation of this number. The exact conversion
from English units to SI units is defined as 1 inch being equivalent to 25.4 mm.
This fraction is already in inches. Multiply by the conversion factor, then also multiply by
the conversion factor for millimeters to meters.
Given the accuracy of the original measurement,
which was determined to have five significant figures, any sig figs in this
converted measurement beyond that are meaningless.
A common way to report an angle is in degrees, minutes, and seconds, or DMS.
Another unit of measure for angles is gradians, or grads. There are 400 grads in one rotation,
which is equal to 360 degrees. The DMS angle shown is going to be converted into grads.
The temptation with significant figures, when dealing with composite units,
is to assume that the number of sig figs will be equal to the number
of decimal places visually represented. While this is appropriate for numbers reported with one unit,
it is not for composite unit numbers. First, convert the measurement to a single type of unit;
more specifically, the smallest unit of the composite. Here it is the second.
There are 60 minutes in one degree, and 60 seconds in one minute.
Convert the degrees and minutes segments of this measurement appropriately.
This number can be adaquately represented with seven significant figures.
If this number, or its converted equivalent, were represented with eight sig figs,
the final decimal place would be a "guess" and falsely imply that the measurement
is more accuracte than it actually was when recorded.
Alternatively, if it were represented with six sig figs, accuracy would be lost.
Continue with part two of this conversion.
If one degree is equal to 60 minutes and one minute equal to 60 seconds,
one degree is equal to 3600 seconds.
Recall that 400 gradians is equivalent to one full rotation, which is also equal to 360 degrees.
Truncate the solution to the appropriate number of significant figures.
Subdivisions of gradians are c's, which are equal to 1/100th of a gradian, and cc's
which are equal to 1/10000th of a gradian. As shown here, separating a decimal gradian
into these subdivisions requires no actual math or conversions.