Basic to the understanding of unit conversion is the understanding
equivalence, the understanding of the multiplicative identity of 1, and how the
two are related.
Review the following table (Webster's New World Dictionary, Second Edition,
Simon and Schuster, 1982) of Standard Units of Conversion to see if you can
create fractions that have a value of 1. You can click to examples following
each table.
1 mil 
0.001 inch 
0.0254 millimeter 
1 inch 
1,000 mils 
2.54 centimeters 
12 inches 
1 foot 
0.3048 meter 
3 feet 
1 yard 
0.9144 meter 
5.5 yards or 16.5 feet 
1 rod (or pole or perch) 
5.029 meters 
1 mile 
5,280 feet 
1.6094 kilometers 
40 rods 
1 furlong 
201.168 meters 
8 furlongs 
1 mile 
1.6094 kilometers 
3 miles 
1 league 
4.83 kilometers 
10 millimeters 
1 centimeters 
0.3937 inch 
10 centimeters 
1 decimeters 
3.937 inches 
10 decimeters 
1 meters 
39.37 inches or 3.20808 feet 
10 meters 
1 decameters 
393.7 inches or 32.8083 feet 
10 decameters 
1 hectometers 
328.083 feet 
10 hectometers 
1 kilometers 
0.621 mile or 3,280 feet 
10 kilometers 
1 myriameter 
6.21 miles 
Example 1. Convert 4.6 miles to feet.
Solution.
 Write 4.6 miles as a fraction by dividing it by 1:
.
 Multiply the fraction
by 1:
 Note: We know that the fraction
is equivalent to 1 because the numerator and the denominator measure the
same length.
 Convert the number 1 in the expression
to the equivalent fraction
so that the expression
can be written as
 Rewrite 4.6 miles as 4.6 x 1 mile and 5280 feet as 5280 x 1 foot, and
rewrite the two fractions as
 Multiply the two fractions:
 Rearrange the numerator:
 Write the above fraction as two fractions:
 Replace the fraction
by 1:
 Simplify:
