Conversion Strategy 2: Unit Analysis

Recall that you need to multiply the original measurement by an appropriate conversion ratio when using the unit analysis strategy.

 

Example 3

How many miles are there in 5000 yards? Express your answer to the nearest hundredth of a mile.

A conversion ratio for yards and miles is 1 mi = 1760 yd , which can also be written as «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac mathcolor=¨#B94A48¨»«mrow»«mn»1«/mn»«mo»§#160;«/mo»«mi»mi«/mi»«/mrow»«mrow»«mn»1760«/mn»«mo»§#160;«/mo»«mi»yd«/mi»«/mrow»«/mfrac»«mo mathcolor=¨#B94A48¨»=«/mo»«mn mathcolor=¨#B94A48¨»1«/mn»«/math» or «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac mathcolor=¨#B94A48¨»«mrow»«mn»1760«/mn»«mo»§#160;«/mo»«mi»yd«/mi»«/mrow»«mrow»«mn»1«/mn»«mo»§#160;«/mo»«mi»mi«/mi»«/mrow»«/mfrac»«mo mathcolor=¨#B94A48¨»=«/mo»«mn mathcolor=¨#B94A48¨»1«/mn»«/math».

Now, multiply the given value by the conversion ratio in the format that will allow for the elimination of the unwanted units.