Units of Conversion

Square (Area) Measure

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.

Square Measure

	1 square inch	6.452
144 square inches	1 square foot	929.03 square centimeters
9 square feet	1 square yard	0.8361 square meter
30.25 square yards	1 square rod	25.292 square meters
160 square rods	1 acre	0.4047 hectare
1 acre	4,840 square yards	43,560 square feet
640 acres	1 square mile	259 hectares
	1 square millimeter	0.00155 square inch
100 square millimeters	1 square centimeter	0.15499 square inch
100 square centimeters	1 square decimeter	15.499 square inches
100 square decimeters	1 square meter	1,549.9 square inches
100 square meters	1 square decameter	119.6 square yards
1 square meters	1 centiare	1.549.9 square inches
100 square decameters	1 square hectometer	2.471 acres
100 centiares	1 are	119.6 square yards
100 ares	1 hectare	2.471 acres
100 hectometers	1 square kilometer	0.386 square mile
100 hectares	0.386 square mile	247.1 acres

Example 1: Convert 180 square inches to square feet.

Solution:

180 square inches can be written as 180 x 1 square inch.
Since 1 square inch can be written as 1 inch x 1 inch,
180 square inches can be written 180 x 1 inch x 1 inch.
Note that 1 inch can be written as 1 inch x 1 and the 1 can be written as a fraction where the numerator and the denominator are equivalent.
Write 1 inch x 1 as 1 inch x $tex2html_wrap_inline257$
This can be further simplified to read $tex2html_wrap_inline259$
180 square inches = 180 x 1 inch x 1 inch = 180 x 1 inch x 1 x 1 inch x 1
= $tex2html_wrap_inline261$

Multiply the fractions. $tex2html_wrap_inline263$

Rearrange the numerator and rearrange the denominator.
$tex2html_wrap_inline265$
Rewrite as five fractions where as many fractions as possible have an equivalent value of 1.
$tex2html_wrap_inline267$ 1.25 x 1 x 1 x 1 foot x 1 foot

Note: 1 foot x 1 foot is the same as one foot squared is the same as one square foot.

The answer is 1.25 square feet.