Units of Conversion

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Linear Measure
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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: tex2html_wrap_inline94 .
  • Multiply the fraction tex2html_wrap_inline96 by 1: tex2html_wrap_inline98
  • Note: We know that the fraction tex2html_wrap_inline100 is equivalent to 1 because the numerator and the denominator measure the same length.
  • Convert the number 1 in the expression tex2html_wrap_inline102 to the equivalent fraction tex2html_wrap_inline104 so that the expression tex2html_wrap_inline102 can be written as tex2html_wrap_inline108
  • Rewrite 4.6 miles as 4.6 x 1 mile and 5280 feet as 5280 x 1 foot, and rewrite the two fractions as tex2html_wrap_inline110
  • Multiply the two fractions: tex2html_wrap_inline112
  • Rearrange the numerator: tex2html_wrap_inline114
  • Write the above fraction as two fractions: tex2html_wrap_inline116
  • Replace the fraction tex2html_wrap_inline118 by 1: tex2html_wrap_inline120
  • Simplify: tex2html_wrap_inline122

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