The Metric System
Learning Objective(s)
· Describe the general relationship between the U.S. customary units and metric units of length, weight/mass, and volume.
· Define the metric prefixes and use them to perform basic conversions among metric units.
In the United States, both the U.S. customary measurement system and the metric system are used, especially in medical, scientific, and technical fields. In most other countries, the metric system is the primary system of measurement. If you travel to other countries, you will see that road signs list distances in kilometers and milk is sold in liters. People in many countries use words like “kilometer,” “liter,” and “milligram” to measure the length, volume, and weight of different objects. These measurement units are part of the metric system.
Unlike the U.S. customary system of measurement, the metric system is based on 10s. For example, a liter is 10 times larger than a deciliter, and a centigram is 10 times larger than a milligram. This idea of “10” is not present in the U.S. customary system—there are 12 inches in a foot, and 3 feet in a yard…and 5,280 feet in a mile!
So, what if you have to find out how many milligrams are in a decigram? Or, what if you want to convert meters to kilometers? Understanding how the metric system works is a good start.
What is Metric?
The metric system uses units such as meter, liter, and gram to measure length, liquid volume, and mass, just as the U.S. customary system uses feet, quarts, and ounces to measure these.
In addition to the difference in the basic units, the metric system is based on 10s, and different measures for length include kilometer, meter, decimeter, centimeter, and millimeter. Notice that the word “meter” is part of all of these units.
The metric system also applies the idea that units within the system get larger or smaller by a power of 10. This means that a meter is 100 times larger than a centimeter, and a kilogram is 1,000 times heavier than a gram. You will explore this idea a bit later. For now, notice how this idea of “getting bigger or smaller by 10” is very different than the relationship between units in the U.S. customary system, where 3 feet equals 1 yard, and 16 ounces equals 1 pound.
Length, Mass, and Volume
The table below shows the basic units of the metric system. Note that the names of all metric units follow from these three basic units.
Length  Mass  Volume 
basic units  
meter  gram  liter 
other units you may see  
kilometer  kilogram  dekaliter 
centimeter  centigram  centiliter 
millimeter  milligram  milliliter 
In the metric system, the basic unit of length is the meter. A meter is slightly larger than a yardstick, or just over three feet.
The basic metric unit of mass is the gram. A regularsized paperclip has a mass of about 1 gram.
Among scientists, one gram is defined as the mass of water that would fill a 1centimeter cube. You may notice that the word “mass” is used here instead of “weight.” In the sciences and technical fields, a distinction is made between weight and mass. Weight is a measure of the pull of gravity on an object. For this reason, an object’s weight would be different if it was weighed on Earth or on the moon because of the difference in the gravitational forces. However, the object’s mass would remain the same in both places because mass measures the amount of substance in an object. As long as you are planning on only measuring objects on Earth, you can use mass/weight fairly interchangeably—but it is worth noting that there is a difference!
Finally, the basic metric unit of volume is the liter. A liter is slightly larger than a quart.



The handle of a shovel is about 1 meter.  A paperclip weighs about 1 gram.  A mediumsized container of milk is about 1 liter. 
Though it is rarely necessary to convert between the customary and metric systems, sometimes it helps to have a mental image of how large or small some units are. The table below shows the relationship between some common units in both systems.
 Common Measurements in Customary and Metric Systems 
Length  1 centimeter is a little less than half an inch. 
 1.6 kilometers is about 1 mile. 
 1 meter is about 3 inches longer than 1 yard. 
Mass  1 kilogram is a little more than 2 pounds. 
 28 grams is about the same as 1 ounce. 
Volume  1 liter is a little more than 1 quart. 
 4 liters is a little more than 1 gallon. 
The metric system is a base 10 system. This means that each successive unit is 10 times larger than the previous one.
The names of metric units are formed by adding a prefix to the basic unit of measurement. To tell how large or small a unit is, you look at the prefix. To tell whether the unit is measuring length, mass, or volume, you look at the base.
Prefixes in the Metric System  
kilo  hecto  deka  meter gram liter  deci  centi  milli 
1,000 times larger than base unit  100 times larger than base unit  10 times larger than base unit  base units  10 times smaller than base unit  100 times smaller than base unit  1,000 times smaller than base unit 
Using this table as a reference, you can see the following:
· A kilogram is 1,000 times larger than one gram (so 1 kilogram = 1,000 grams).
· A centimeter is 100 times smaller than one meter (so 1 meter = 100 centimeters).
· A dekaliter is 10 times larger than one liter (so 1 dekaliter = 10 liters).
Here is a similar table that just shows the metric units of measurement for mass, along with their size relative to 1 gram (the base unit). The common abbreviations for these metric units have been included as well.
Measuring Mass in the Metric System  
kilogram (kg)  hectogram (hg)  dekagram (dag) 
gram (g)
 decigram (dg)  centigram (cg)  milligram (mg) 
1,000 grams  100 grams  10 grams  gram  0.1 gram  0.01 gram  0.001 gram 
Since the prefixes remain constant through the metric system, you could create similar charts for length and volume. The prefixes have the same meanings whether they are attached to the units of length (meter), mass (gram), or volume (liter).
Which of the following sets of three units are all metric measurements of length?
A) inch, foot, yard
B) kilometer, centimeter, millimeter
C) kilogram, gram, centigram
D) kilometer, foot, decimeter

Converting Units Up and Down the Metric Scale
Converting between metric units of measure requires knowledge of the metric prefixes and an understanding of the decimal system—that’s about it.
For instance, you can figure out how many centigrams are in one dekagram by using the table above. One dekagram is larger than one centigram, so you expect that one dekagram will equal many centigrams.
In the table, each unit is 10 times larger than the one to its immediate right. This means that 1 dekagram = 10 grams; 10 grams = 100 decigrams; and 100 decigrams = 1,000 centigrams. So, 1 dekagram = 1,000 centigrams.
Example  
Problem  How many milligrams are in one decigram?  

 Identify locations of milligrams and decigrams.  

 Decigrams (dg) are larger than milligrams (mg), so you expect there to be many mg in one dg.  

 Dg is 10 times larger than a cg, and a cg is 10 times larger than a mg.
Since you are going from a larger unit to a smaller unit, multiply.  
 1 dg · 10 · 10 = 100 mg  Multiply: 1 · 10 · 10, to find the number of milligrams in one decigram.  
Answer  There are 100 milligrams (mg) in 1 decigram (dg). 
Example  
Problem  Convert 1 centimeter to kilometers.  

 Identify locations of kilometers and centimeters.  

 Kilometers (km) are larger than centimeters (cm), so you expect there to be less than one km in a cm.
 

 Cm is 10 times smaller than a dm; a dm is 10 times smaller than a m, etc.
Since you are going from a smaller unit to a larger unit, divide.  
 1 cm ÷ 10 ÷ 10 ÷ 10 ÷ 10 ÷ 10 = 0.00001 km  Divide: 1 ÷ 10 ÷ 10 ÷ 10 ÷ 10 ÷ 10, to find the number of kilometers in one centimeter.  
Answer  1 centimeter (cm) = 0.00001 kilometers (km). 
Once you begin to understand the metric system, you can use a shortcut to convert among different metric units. The size of metric units increases tenfold as you go up the metric scale. The decimal system works the same way: a tenth is 10 times larger than a hundredth; a hundredth is 10 times larger than a thousandth, etc. By applying what you know about decimals to the metric system, converting among units is as simple as moving decimal points.
Here is the first problem from above: How many milligrams are in one decigram? You can recreate the order of the metric units as shown below:
_{}
This question asks you to start with 1 decigram and convert that to milligrams. As shown above, milligrams is two places to the right of decigrams. You can just move the decimal point two places to the right to convert decigrams to milligrams: _{}.
The same method works when you are converting from a smaller to a larger unit, as in the problem: Convert 1 centimeter to kilometers.
_{}
Note that instead of moving to the right, you are now moving to the left—so the decimal point must do the same: _{}.
How many milliliters are in 1 liter?
A) 0.001
B) 0.1
C) 100
D) 1,000

Summary
The metric system is an alternative system of measurement used in most countries, as well as in the United States. The metric system is based on joining one of a series of prefixes, including kilo, hecto, deka, deci, centi, and milli, with a base unit of measurement, such as meter, liter, or gram. Units in the metric system are all related by a power of 10, which means that each successive unit is 10 times larger than the previous one. This makes converting one metric measurement to another a straightforward process, and is often as simple as moving a decimal point. It is always important, though, to consider the direction of the conversion. If you are converting a smaller unit to a larger unit, then the decimal point has to move to the left (making your number smaller); if you are converting a larger unit to a smaller unit, then the decimal point has to move to the right (making your number larger).