Converting within the Metric System

 

Learning Objective(s)

·         Perform arithmetic calculations on metric units of length, mass, and volume.

 

 

While knowing the different units used in the metric system is important, the real purpose behind learning the metric system is for you to be able to use these measurement units to calculate the size, mass, or volume of different objects. In practice, it is often necessary to convert one metric measurement to another unit—this happens frequently in the medical, scientific, and technical fields, where the metric system is commonly used.

 

If you have a prescription for 5,000 mg of medicine, and upon getting it filled, the dosage reads 5 g of medicine, did the pharmacist make a mistake?

 

For a moment, imagine that you are a pharmacist. You receive three prescriptions for liquid amoxicillin: one calls for 2.5 centiliters, one calls for 0.3 deciliters, and one calls for 450 milliliters. Amoxicillin is stored in the refrigerator in 1 liter, 1 deciliter, and 1 centiliter containers. Which container should you use to ensure you are not wasting any of the unused drug?

 

To solve this problem, you need to know how to convert from one measurement to another as well as how to add different quantities together. Let’s take a look at how to do this.

 

 

Converting between measurements in the metric system is simply a matter of identifying the unit that you have, the unit that you want to convert to, and then counting the number of units between them. A basic example of this is shown below.

 

 

This problem is straightforward because you are converting 1 kilometer to another unit. The example below shows how you would solve this problem if you were asked to convert 8.2 kilometers to decimeters. Notice that most steps are the same; the critical difference is that you multiply by 8.2 in the final step.

 

 

You can also apply the rules of base 10 to use the “move the decimal” shortcut method in this example. Notice how decimeters (dm) is four places to the right of kilometers (km); similarly, you move the decimal point four places to the right when converting 8.2 kilometers to decimeters.

 

 

 

 

How many dekaliters are in 0.5 deciliters?   A) 500   B) 5   C) 0.5   D) 0.005   Show/Hide Answer A) 500 Incorrect. A dekaliter is larger than a deciliter, so you would expect the number of dekaliters in 0.5 deciliters to be smaller than 0.5. The correct answer is 0.005.   B) 5 Incorrect. A dekaliter is larger than a deciliter, so you would expect the number of dekaliters in 0.5 deciliters to be smaller than 0.5. The correct answer is 0.005.   C) 0.5 Incorrect. Deciliters and dekaliters are different units of measurement, so you would not expect 0.5 deciliters to equal 0.5 dekaliters. The correct answer is 0.005.   D) 0.005 Correct. One deciliter is 100 times smaller than a dekaliter, so you move the decimal point two places to the left to convert 0.5 deciliters to 0.005 dekaliters.

 

 

 

 

You can use similar processes when converting from smaller to larger units. When converting a larger unit to a smaller one, you multiply; when you convert a smaller unit to a larger one, you divide. Here is an example.

 

 

Notice that the shortcut method of counting prefixes and moving the decimal the same number of places also works here. Just make sure you are moving the decimal point in the correct direction for the conversion.

 

 

 

Convert 3,085 milligrams to grams.   A) 3,085,000 grams   B) 308.5 grams   C) 3.085 grams   D) 0.3085 grams   Show/Hide Answer A) 3,085,000 grams Incorrect. Grams are larger than milligrams, so you would expect the number of grams in 3,085 milligrams to be less than 3,085. The correct answer is 3.085 grams.   B) 308.5 grams Incorrect. One gram is more than 10 times larger than a milligram, so you would expect the number of grams to be less than 308.5. The correct answer is 3.085 grams.   C) 3.085 grams Correct. One gram is 1,000 times larger than a milligram, so you can move the decimal point in 3,085 three places to the left.     D) 0.3085 grams Incorrect. This is too small; one gram is 1,000, not 10,000, times larger than a milligram. The correct answer is 3.085 grams.

 

 

 

There is yet another method that you can use to convert metric measurements—the factor label method. You used this method when you were converting measurement units within the U.S. customary system.

 

The factor label method works the same in the metric system; it relies on the use of unit fractions and the cancelling of intermediate units. The table below shows some of the unit equivalents and unit fractions for length in the metric system. (You should notice that all of the unit fractions contain a factor of 10. Remember that the metric system is based on the notion that each unit is 10 times larger than the one that came before it.)

 

Also, notice that two new prefixes have been added here: mega- (which is very big) and micro- (which is very small).

 

 

When applying the factor label method in the metric system, be sure to check that you are not skipping over any intermediate units of measurement!

 

 

 

Using whichever method you prefer, convert 32.5 kilometers to meters.   A) 32,500 m   B) 325 m   C) 0.325 m   D) 0.00325 m   Show/Hide Answer A) 32,500 m Correct. To find the number of m in 32.5 km, you can set up the following equation: . The km units cancel, leaving the answer in m.   B) 325 m Incorrect. A km is more than 10 times the size of a m; look at the unit fractions and try your calculations again. The correct answer is 32,500 m.   C) 0.325 m Incorrect. A km is larger than a meter, so you would expect the number of meters in 32.5 km to be more than 32.5. Look at the unit fractions and try your calculations again. The correct answer is 32,500 m.   D) 0.00325 m Incorrect. A km is larger than a meter, so you would expect the number of meters in 32.5 km to be more than 32.5. Look at the unit fractions and try your calculations again. The correct answer is 32,500 m.

 

Now that you have seen how to convert among metric measurements in multiple ways, let’s revisit the problem posed earlier.

 

 

 

 

To convert among units in the metric system, identify the unit that you have, the unit that you want to convert to, and then count the number of units between them. If you are going from a larger unit to a smaller unit, you multiply by 10 successively. If you are going from a smaller unit to a larger unit, you divide by 10 successively. The factor label method can also be applied to conversions within the metric system. To use the factor label method, you multiply the original measurement by unit fractions; this allows you to represent the original measurement in a different measurement unit.