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Metric System and Unit Conversion

Metric System Unit System of Measurement

The Metric system was developed in France during the Napoleonic reign of France in the 1790's. The metric system has several advantages over the English system which is still in place in the U.S. However the scientific community has adopted the metric system almost from its inception. In fact, the metric system missed being nationalized in this country by one vote in the Continental Congress in the late 1700's or early 1800's. The advantages of the Metric system are:

    It was based on a decimal system (ie:powers of ten). Therefore, it simplifies calculations by using a set of prefixes which we will discuss in a few minutes.

    It is used by most other nations of the world, and therefore, it has commercial and trade advantage. If an American manufacturer that has domestic and international customers is to compete, they have to absorb the added cost of dealing with two systems of measurement.

Let's now take a few minutes and speak of the useful set of "prefixes" used in the metric system sometimes referred to as the System Internationale (SI). One of the mathematical advantages of the metric system is its combination of metric terminology with its decimal organization. There are several prefixes that are associated with a decimal position and can be attached to the base metric unit in order to create a new metric unit. The knowledge of the decimal meaning of the prefix establishes the relationship between the newly created unit and the base unit.

For example: the prefix "kilo" means 103 or 1000 so if I take a mythical base unit like the "bounce" and I attach the kilo prefix in front, I create a new unit called the "kilobounce".

In addition, the relationship between the two units is now well established. Since I know that "kilo" means 1000 then one kilobounce unit is the same as (or equal to) 103 bounce units. The prefixes that are most important are listed below along with their decimal and exponential equivalents:

 Prefix        decimal equivalent     exponential equivalent

 Pico            0.000000000001            10-12

 Nano              0.000000001             10-9

 Micro             0.000001                10-6

 Milli             0.001                   10-3

 Centi             0.01                    10-2

 Deci              0.1                     10-1

 no prefix         1.0                     100

 Deka             10.0                     101

 Hecto           100.0                     102

 Kilo           1000.0                     103

 Mega      1,000,000.                      106

 Giga  1,000,000,000.                      109

There are several dozen prefixes used but these above are most commonly used in Science measurements. Today, we will be looking at the metric units of measurement in five separate areas of measure. The abreviations of each unit will appear in parenthesis when the unit is first mentioned in the lesson. The types of measure discussed in this mini-lesson are :

  1. Mass

  2. Dimension

  3. Volume

  4. Time

  5. Area

The last two will be briefly dealt with.

Mass Measurement

The measure of mass in the metric system has several units that scientists use most often.

The kilogram is the standard unit of mass in the metric or SI system. The Kilogram(Kg) is roughly analogous to the English pound. It takes approximately 2.12 pounds to equal one Kilogram.

A smaller mass unit analogous to the English ounce is the gram. The gram represents approx. 30 dry ounces in mass. Other metric mass units include:

  1. the centigram (cg)

  2. milligram(mg)

  3. microgram (µg)

  4. nanogram(ng).

Question: What are the relationship of each of the above mass units with the base gram unit? Write each of them down.

Click here if you wish to check your answers.

The basic instrument used to measure mass is the mass balance. There are some digital balances today that can display the mass of an object in several different mass units both in the English and Metric systems

Dimensional Measurement

Now let us go over dimensional measurement that is measure of length, width, and height. The basic metric unit of dimension is the meter (m). The meter is analogous to the English yard. A meter is equal to slightly more than a yard (about 10% larger).

One meter is equal to 1.09 yards or 39.36 inches.

A larger metric unit used often is the kilometer(km) which is analogous to the English mile. One kilometer is equal to 0.62 miles. In countries where the metric system is the national standard, signposts and posted speed limits are in km or km per hour. For example, the most common speed limit in Mexico is 100, but that is 100 km/h or about 60 miles per hour!!

Other dimensional units include the

  1. decimeter(dm)

  2. centimeter(cm) which is analogous to the English inch. One inch is equal to 2.54 cm

  3. millimeter(mm)

  4. micrometer(µm)

  5. nanometer(nm). The nanometer is used when very small interatomic or intermolecular distances are called for.

The main instrument in the science lab that measures dimension is the metric ruler. The metric ruler comes in various sizes. There is the 150 mm ruler and a metric meter ruler which are used most. However, all metric rulers are calibrated the same. The numerically numbered positions(major calibrations) are equal to centimeter marks, and then there are ten equally spaced positions(minor calibrations) in between each of the numbered positions each of which are equal to 0.1 cm(1 mm). According to this calibration, one can record measurements with one position of estimation to the nearest 0.01 cm.

Another instrument most often used in Physics labs is called a micrometer. As the name implies it can measure to the nearest micrometer and is used for very precise measurements of diameters.

Volume Measurement

The third type of measure is measure of volume. Actually we can break this down into the measure of

  1. solid volume (regular and irregular)
  2. fluid (liquid and gas) volume

Volumes of Regular Solids

Regular Solids are those that have well defined dimensions of length, width, height, and diameter. These can first be measured with a suitable dimensional instrument like a metric ruler. Then a suitable geometrical formula might be applied to get the volume.

For example, if the solid was rectangular shaped, you would measure the dimensions of the rectangle and then use the formual V = l X w X h in order to determine the volume of the rectangle.

Volumes of Irregular Solids

Irregularly shaped solids do not have well defined dimensions and therefore can't use the above method of determining its volume. However, one can use the principle of liquid displacement that says since two chucks of matter can't occupy the same space at the same time that when placed together one object will displace the other. If we measure a certain volume of water in a graduated cylinder to be 5.0 cm3, and we immerse some pieces of metal into the water, the reading on the graduated cylinder might read 14.0 cm3. By subtracting the two readings we now have how much displacement of the water there was when the metal fragments were immersed. That displacement would be equal to the volume of the metal fragments.

14.0 - 5.0 = 9.0 cm3 = volume of metal fragments

Measurement of Fluid Volumes

Let's now discuss measure of fluid volume. There are several instruments used to directly measure fluid volumes. The graduated cylinder is the most commonly used in the lab. However, there are several others. The pipet, buret,and volumetric Flask measure fluid volumes more precisely than most graduated cylinders.

The basic metric unit of measure for volume is the liter(l) unit. The liter is analogous to the English quart. One liter being the same as 1.06 quarts. It is basically a fluid volume unit as is the smaller metric unit called the milliliter(ml). The milliliter is analogous to the English fluid ounce. One fluid ounce is equal to about 30 ml.

Other metric units of volume that are more often associated with volumes of solids is the cubic centimeter(cm3) which is equal to a milliliter. To a careless observer the cm3 may look like a dimensional unit since it has the symbol for "centimeter" in it. However, it also has the word "cubic" which always indicates a volume unit.

You can think of a cubic centimeter as a cube 1 cm on each edge. The volume of such a cube would be 1cm X 1cm X 1cm or 1 cm3.

We also use the cubic meter(m3) often in science to measure large volumes in space.

Actually, any dimensional relationship such as 100 cm = 1 m can be used to derive a volume unit relationship simply by cubeing BOTH sides of the relationship so for example:

100 cm = 1 m cubed would be:

(100 cm)(100 cm)(100 cm) = (1m)(1m)(1m) or 1 X 106 cm3 = 1 m3

You can even do this with English dimensional relationships that result in a newly created volume relationship. For example:

1 ft = 12 in. If we cubed both sides we would have:

(1 ft)(1 ft)(1 ft)= (12 in)(12 in)(12in) or 1 ft3 = 1728 in3

Try it yourself on the following dimensional relationships:

1 inch = 2.54 cm Determine the relationship between cubic inches and cubic centimeters?

Click here if you wish to check your results

Area Measurement

Area measurement relationships are similar to volume relationships except you square both sides of the dimensional relationship. For example if we wanted to know the relationship between square cm and square m we could begin with the following dimensional relationship between cm and m

100 cm = 1 m

Now square bothe sides

(100 cm)2 = (1 m)2

10000 cm2 = 1 m2

In summary, dimensional measurement is one dimensional, area measurement is two dimensional and volume measurement is three dimensional in scope.

Here is a set of problems for you to try:

  1. The instrument designed to measure dimension is the _________ ________

  2. The graduated cylinder is an instrument that measures

    _____________.

    Picture of graduated cylinder

  3. The prefix that signifys 0.001 is __________

  4. The prefix that signifys 1 X 106 is ________

  5. The english unit associated with the meter is ________

  6. 1 meter = _________mm

  7. A cubic centimeter is a unit of ___________

  8. The kilogram is associated with the English unit ________

  9. Giga prefix signifys what decimal equivalent (place in exponential notation _____________

  10. One pico second would be how much of a second (express in exponential notation) ______________

  11. If 1 meter = 100 cm, then what is the relationship between m3 and cm3? Show work.

Check for the correct answers

If you would like more information on the metric system then visit the U.S. Metric Association for further information.

If you would like a conversion table please visit:

Metric Conversion Table

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R. H. Logan, Instructor of Chemistry, Dallas County Community College District, North Lake College.

Page last revised 7/9/2005 

All contents copyrighted (c) 1995
R.H. Logan, Instructor of Chemistry,DCCCD
All Rights reserved



What are the relationship of each of the following mass units with the base gram unit? Write each of them down.


    

  • the centigram (cg)
    

  • milligram(mg)
    

  • microgram (µg)
    

  • nanogram(ng).



Answers


the centigram (cg) = 10-2 gram since centi means 10-2


milligram(mg) = 10-3 gram since milli means 10-3


microgram (µg) = 10-6 gram since micro means 10-6


nanogram(ng) = 10-9 gram since nano means 10-9


Click here to return to the metric system lesson. 



1 inch = 2.54 cm Determine the relationship between cubic inches and cubic centimeters?


cube both sides


(1 inch)3 = (2.54 cm)3


1 in3 = 16.39 cm3


Click here to return to the metric system lesson. 





Correct answers to Homework




    

  1. The instrument designed to measure dimension is the 
    METRIC RULER
    


  2. The graduated  cylinder is an instrument that measures
     
    VOLUME.
    

Picture of graduated cylinder
    

  3. The prefix that signifys 0.001 is MILLI
    


  4. The prefix that signifys 1 X 106 is MEGA
    


  5. The english unit associated with the meter is YARD
    


  6. 1 meter = 1000 mm
    


  7. A cubic centimeter is a unit of VOLUME
    


  8. The kilogram is associated with the English unit POUND
    


  9. Giga prefix signifys what decimal equivalent (place in exponential notation 1 X 109
    


  10. One pico second would be how much of a second (express in exponential notation) 1 X 10-12 sec
    


  11. If 1 meter = 100 cm, then what is the relationship between m3 and cm3? Show work.
    
(1 meter)3 = (100)3

    
1 m3 = 1 X 106 cm3




Return to the lesson

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