# Metric System Conversions

The metric system is recognized globally as the system of units for measuring length, liquid volume, and mass. The system customarily used in the United States is completely different; however, we rely on the metric system in many technical, medical, and scientific applications. As you will see in this video, understanding the metric system can be quite simple if you learn the terminology and structure of converting between metric units.

Hectogram, Centigram, Decagram….

Those words may seem foreign and a bit intimidating until you recognize a very important pattern. Notice that all three words include a prefix before the word “gram”, which is the basic unit for mass, or weight, in the metric system. The prefix is the information that you need to determine whether the unit is smaller or larger than the basic unit of measure. The other basic units of measure for the metric system are meter, to measure length and distance; and liter, to measure liquid volume. These units are named in a similar way.

So, once you know the unit that is being measured, understanding the prefix is essential. Metric units follow a base “10” system, meaning that converting between units will simply be a matter of **multiplying** or **dividing** by 10.

Prefix | Value | Multiple/Fraction of 10 | Scientific Notation |

Kilo | 1000 | 10 × 10 × 10 | 10^{3} |

Hecto | 100 | 10 × 10 | 10^{2} |

Deca | 10 | 10 | 10^{1} |

Basic Unit:gram, meter, liter | 1 | 1 | 10^{0} |

Deci | .10 | \(\frac{1}{10}\) | 10^{-1} |

Centi | .01 | \(\frac{1}{100}\) | 10^{-2} |

Milli | .001 | \(\frac{1}{1000}\) | 10^{-3} |

This table shows the ordering of the prefixes in relationship to the basic unit, along with the numeric value, multiple or fraction of 10, and its representation in scientific notation. To read this table, start at the prefix and determine how much smaller or larger it is to the base unit. For example, the base unit of a meter is 100 times larger than a centimeter. Conversely, for every meter, there are 100 centimeters.

The order of the prefixes is very important, as it indicates whether the metric system unit is larger or smaller than the basic unit. Once the order is known, you can easily convert between base units by moving the decimal point either to the right, for a larger unit, or to the left, for a smaller unit. Let’s look at a few examples:

Ex 1: In our first example we’re going to convert 2 liters to milliliters

You are being asked to convert the basic measurement of volume to a smaller unit. As a result, the number of milliliters will be a larger number. A liter is 1000 times larger than a milliliter, so multiply 2 times 1,000 to give you 2,000 milliliters.

To consider the decimal point approach, you will need to move the decimal point three places to the right to make the conversion from a larger unit to a smaller unit.

Ex 2: In example 2 we’re going to convert 5 grams to decagrams

In this example, you are being asked to convert the base unit of weight to a larger unit. A gram is 10 times smaller than a decagram, so divide 5 by 10 to get 0.5

Moving the decimal point one place to the left would also achieve the same result to convert from a smaller unit to a larger unit.

To convert between units other than the base, the strategy is the same. Simply work your way around the table in multiples or fractions of 10 to get to the desired unit. Here are a few examples:

Ex 3: Convert 2 kilometers to centimeters

Clearly, this is going to be a very large number, as a **centimeter** is a fraction of a **meter**, which is a fraction of a **kilometer**. To do this conversion, start at the smaller unit and count how many times you have to multiply by 10 to get to the larger unit. There are five multiples of ten separating a centimeter from a kilometer on the table. Therefore, 2 kilometers converts to centimeters as follows: 2 times 10 to the 5th power, equals 2 times 100,000; equals 200,000.

2 × 10^{5}= 2 × 100,000 = 200,000 centimeters

There are 200,000 centimeters in 2 kilometers. You can also do this conversion quickly by moving the decimal 5 places to the right.

Ex 4: Convert 6 milligrams to decigrams

This conversion goes in an opposite direction, as a decigram is larger unit than a milligram. Rather than multiplying, you will divide by the number of “tens” that separate the decigrams and milligrams on the table: 6 times 10 to the negative 2 power is equal to, 6 times 1 over 10, which is equal to 0.06.

6 × 10^{-2} = 6 × \(\frac{1}{100}\) = .06 decigrams

There are .06 decigrams in 6 milligrams. As you can see, the decimal point was moved one, two places to the left to get to the smaller quantity.

So, to review, the metric system units are clearly defined by quantitative prefixes that are related by the convenient base of 10. The trick is in knowing the meaning of the prefixes, which reveal whether the unit is larger or smaller than the base. Keeping a table of the prefixes at hand and remembering the direction to move the decimal point simplifies the process of converting between units.

I hope this review was helpful! Thanks for watching, and happy studying!

## Practice Questions

**Question #1:**

What are the metric base units for length, volume, and mass?

Length: Feet, Volume: Pounds, Mass: Grams

Length: Liters, Volume: Meters, Mass: Grams

Length: Meters, Volume: Liters, Mass: Grams

Length: Miles, Volume: Gallons, Mass: Pounds

**Answer:**

There are three basic units of measure in the metric system. Meters are used to measure length, liters are used to measure volume, and grams are used to measure mass. All three of these units of measure are based on powers of ten. For example, a liter is 10 times larger than a deciliter.

**Question #2:**

Fill in the blank: 6,544 meters is equivalent to _______ kilometers.

0.6544

65.22

6.522

6.544

**Answer:**

Kilometers are 1,000 times larger than meters. This means that there will be 1,000 times as many meters as kilometers. If there are 6,544 meters, there will be 1,000 times fewer kilometers. 6,544 meters divided by 1,000 equals 6.544 kilometers.

**Question #3:**

Which is the largest amount?

600 grams

4 kilograms

3.692 milligrams

600 centigrams

**Answer:**

When comparing metric values, it can be helpful to convert each number into its base unit in order to make a direct comparison. In this problem, we need to convert each number into grams in order to make this direct comparison. For example, 4 kilograms is the same as 4,000 grams. 3.692 milligrams is 0.003692 grams. 600 centigrams is the same as 6 grams. 600 grams is already expressed in base units so it does not need to be adjusted. Now that all of the values are in the same unit, it is clear that 4,000 grams (4 kilograms) is the largest amount.

**Question #4:**

Sybil purchases a 2 liter bottle of orange juice to share with her family. She pours 600 milliliters into a glass for her brother. How much orange juice is still left in the bottle?

1,400 milliliters

1,000 milliliters

1.5 liters

1.6 liters

**Answer:**

2 liters is equivalent to 2,000 milliliters. The large bottle of juice originally holds 2,000 milliliters of juice. There are 1,400 milliliters left in the bottle after 600 milliliters are poured out.

**Question #5:**

Carson rode 2 kilometers on his bike. His sister Sam rode 3,000 meters on her bike. Who rode farther, and by how much?

Sam rode 1 kilometer farther than Carson.

Carson rode 1 kilometer farther than Sam.

Sam rode 1,000 kilometers farther than Carson.

Carson rode 1,000 kilometers farther than Sam.

**Answer:**

Carson rode his bike 2 kilometers, which is the same as 2,000 meters. Sam rode her bike 3,000 meters. 3,000 meters take away 2,000 meters equals 1,000 meters, which is the same as 1 kilometer.