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:
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