You can solve almost any conversion problem using a unit cancelling method known as dimensional analysis. Use the relationship between units as a ratio. For example, the number of milliliters in a liter would expressed as either 1 liter/1,000 milliliters, or 1,000 milliliters/1 liter, depending on the needs of the conversion. All numbers are laid out so that their units cancel, leaving the desired number in correct units. For example, if you want to know how many milliliters are in 3 liters, write (3 liters) x (1,000 milliliters/1 liter). When the two uses of "liter" cancel each other, and we do the multiplication, we get the correct answer: 3,000 milliliters.

## Example of a Metric Liquid Conversion

Suppose you measure 33.0 milliliters of water and need to know the measurement in centiliters. Use the relationships that you know: 1 liter contains 100 centiliters and 1 liter contains 1,000 milliliters. Write out (33.0 milliliters) x (1 liter/1,000 milliliters) x (100 centiliters/1 liter), then cancel the units and multiply to get 330 centiliters. If the unit cancellation had not yielded the units you sought -- centiliters -- you would know that one or more of your ratios are upside-down and could adjust the equation accordingly.

## Example of a U.S. Liquid Conversion

The same unit cancelling method may be used with U.S. measurements. If you are cooking muffins and need ½ cup of oil but only have teaspoons to measure with, you need to find out how many teaspoons make up 1/2 cup. In this case, you could use the measurement ratios available in your cookbook and write out (½ cup) x (16 tablespoons/1 cup) x (3 teaspoons/1 tablespoon). When all the units cancel correctly to yield tablespoons, so we do the multiplication to get 24 teaspoons.

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About the Author

Ashley K. Ezell is a certified high school science teacher of 16 years with experience in grades seven through twelve. In addition to teaching in the public school setting, Ezell is also an online science instructor for the Alabama State Department of Education. With a Bachelor of Science in comprehensive science education and a Master of Education in instructional technology from Troy University in Alabama, Ezell has a wealth of knowledge and experience in the education field.

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