Conversion Strategy 2: Unit Analysis

In this method of unit conversion you will multiply by a conversion ratio that will allow you to eliminate unwanted units.

 

Example 2

Convert 5500 decimetres into hectometres.

Begin by determining a conversion ratio for the two units. Using the Prefix table, you can see that 10 dm = 0.01 hm or that «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac mathcolor=¨#B94A48¨»«mrow»«mn»10«/mn»«mo»§#160;«/mo»«mi»dm«/mi»«/mrow»«mrow»«mn»0«/mn»«mo».«/mo»«mn»01«/mn»«mo»§#160;«/mo»«mi»hm«/mi»«/mrow»«/mfrac»«mo mathcolor=¨#B94A48¨»=«/mo»«mn mathcolor=¨#B94A48¨»1«/mn»«/math» and «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac mathcolor=¨#B94A48¨»«mrow»«mn»0«/mn»«mo».«/mo»«mn»01«/mn»«mo»§#160;«/mo»«mi»hm«/mi»«/mrow»«mrow»«mn»10«/mn»«mo»§#160;«/mo»«mi»dm«/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. Remember that the conversion ratio is equal to 1, so switching the numerator and denominator has no impact on the value.

If you pick the wrong format for the conversion ratio, the unwanted units will not be eliminated and you will know immediately that you've made an error. The following shows a setup where the unwanted units will not be eliminated.