D. Converting Between SI Units

Conversion Strategy 1: Use a Proportion

A proportion is a statement of equality between two ratios. Proportions can be used to convert between any pair of units for which a conversion ratio is known.

Proportion

A statement of equality between two ratios.

Ratio

A relationship between two quantities. A ratio is often expressed as a fraction.

 

A video demonstration of Example 1 is provided.

 

Example 1

Convert 75 kL into cL.

Begin by determining a conversion ratio for the two units. Using the Prefix table, note that «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn mathcolor=¨#B94A48¨»0«/mn»«mo mathcolor=¨#B94A48¨».«/mo»«mn mathcolor=¨#B94A48¨»001«/mn»«mo mathcolor=¨#B94A48¨»§#160;«/mo»«mi mathcolor=¨#B94A48¨»kL«/mi»«mo mathcolor=¨#B94A48¨»§#160;«/mo»«mo mathcolor=¨#B94A48¨»=«/mo»«mo mathcolor=¨#B94A48¨»§#160;«/mo»«mn mathcolor=¨#B94A48¨»100«/mn»«mo mathcolor=¨#B94A48¨»§#160;«/mo»«mi mathcolor=¨#B94A48¨»cL«/mi»«/math» or that «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»001«/mn»«mo»§#160;«/mo»«mi»kL«/mi»«/mrow»«mrow»«mn»100«/mn»«mo»§#160;«/mo»«mi»cL«/mi»«/mrow»«/mfrac»«mo mathcolor=¨#B94A48¨»§#160;«/mo»«mo mathcolor=¨#B94A48¨»=«/mo»«mo mathcolor=¨#B94A48¨»§#160;«/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»100«/mn»«mo»§#160;«/mo»«mi»cL«/mi»«/mrow»«mrow»«mn»0«/mn»«mo».«/mo»«mn»001«/mn»«mo»§#160;«/mo»«mi»kL«/mi»«/mrow»«/mfrac»«mo mathcolor=¨#B94A48¨»§#160;«/mo»«mo mathcolor=¨#B94A48¨»=«/mo»«mo mathcolor=¨#B94A48¨»§#160;«/mo»«mn mathcolor=¨#B94A48¨»1«/mn»«/math».

The expression «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mn»75«/mn»«mo»§#160;«/mo»«mi»kL«/mi»«/mrow»«mrow»«mi»x«/mi»«mo mathvariant=¨italic¨»§#160;«/mo»«mi»cL«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mn»1«/mn»«/math» can also be used here. However, expressions with a variable in the denominator are often harder to work with.

Let x represent the unknown number of centiliters.

Then, «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathcolor=¨#B94A48¨»x«/mi»«mo mathcolor=¨#B94A48¨»§#160;«/mo»«mi mathcolor=¨#B94A48¨»cL«/mi»«mo mathcolor=¨#B94A48¨»§#160;«/mo»«mo mathcolor=¨#B94A48¨»=«/mo»«mo mathcolor=¨#B94A48¨»§#160;«/mo»«mn mathcolor=¨#B94A48¨»75«/mn»«mo mathcolor=¨#B94A48¨»§#160;«/mo»«mi mathcolor=¨#B94A48¨»kL«/mi»«/math» and «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac mathcolor=¨#B94A48¨»«mrow»«mi»x«/mi»«mo»§#160;«/mo»«mi»cL«/mi»«/mrow»«mrow»«mn»75«/mn»«mo»§#160;«/mo»«mi»kL«/mi»«/mrow»«/mfrac»«mo mathcolor=¨#B94A48¨»§#160;«/mo»«mo mathcolor=¨#B94A48¨»=«/mo»«mo mathcolor=¨#B94A48¨»§#160;«/mo»«mn mathcolor=¨#B94A48¨»1«/mn»«/math».


Now there are two expressions equal to 1, so they must be equal to each other. This allows you to set up a proportion. Choose the conversion ratio format that has the same unit location as the expression with the variable. This will allow for a proper conversion.

Now solve the equation to determine the value of x.

Often the units are not shown with the variable and "x" is written instead of "x cL."

When the same value or unit shows up in the numerator and the denominator, the units are eliminated.

Notice that the kilolitre units are eliminated on both sides of the equation to leave just the centilitre units.