"Scientific" Measurement /

System Internationale /

The Metric System

Most people around the world don't learn ounces, pounds, tons, pints, gallons, inches (& fractions), yards, and miles, with all of the different conversion factors - they use the System Internationale (SI), also known as the metric system. Even England, where our English system originated, uses SI, and our own U.S. official measurements are defined using SI units.

Why is SI so popular? One major reason is that, once you learn a basic unit, larger and smaller versions always follow the same rules for size and naming, based on powers of ten and standard prefixes. The basic prefixes are given on the chart below, with some common units and the most used prefixes highlighted in bold:

Prefix         Symbol     Meaning         Base Unit Multiplied by              Factor
tera-                T             trillion               1,000,000,000,000                    1012

giga-               g             billion                1,000,000,000                           109

mega-            M             million                 1,000,000                                 106

kilo-                k              thousand               1,000                                      103

hecto-              h             hundred                   100                                       102

deca-             da            ten                             10                                         101

single units, no prefix - Examples: meter, liter, gram 100

deci-               d              tenth                         0.1                                         10-1

centi-              c              hundredth               0.01                                        10-2

milli-               m              thousandth            0.001                                       10-3

micro-            u               millionth               0.000001                                  10-6

nano-               n               billionth           0.000000001                                10-9

pico-                p               trillionth         0.00000000001                             10-12

What's it all mean?
A kilometer is a thousand meters, a kiloliter is a thousand liters, a kilogram is a thousand grams; a centimeter is a hundredth of a meter, a centiliter is a hundredth of a liter, a centigram is a hundredth of a gram. The prefixes can be applied to any kind of unit. Only temperature degrees (Celsius or Kelvin in SI) seem to be exempt. Also, there is no accepted metric time system in use.

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Measurement Lab

How Different Types of Units are Related

A somewhat odd feature of SI is that most of the units are defined by using logical applications of other units, so you get unusual but useful cross-connections. Below are several examples:

A liter of pure water by definition has a mass/weight of one kilogram.

A cubic centimeter (a cube one centimeter on each side) contains the same space as a milliliter (a unit of liquid volume).

A calorie (not our English Calorie, which is actually an SI kilocalorie) is defined as the amount of heat required to raise one gram of water one degree Celsius.

"Ballpark" Figuring

Learning a system you didn't grow up with is very difficult, and most late U.S. exercises in SI is all formal and precise. However, you can "get by" with metric conversions by remembering a few easy "ballpark" figures that will give you an approximate changeover from one system to the other. The conversions are meant to be sloppy and imprecise, done in the head for the most part...

Length. A meter is close to a yard, for short distances - for longer distances, it's useful to remember that it's about a yard-and-a-tenth. A kilometer is very close to six-tenths of a mile ( a 10-k race is really close to six miles), but a mile is enough over a kilometer-and-a-half to make those conversions very fuzzy. An inch is almost exactly two-and-a-half centimeters, which makes a foot about 30 centimeters.

Mass / Weight. A kilogram is about two-and-a-quarter pounds. A weight ounce (not the same as a volume ounce!!!) is about 30 grams. A metric tonne, 1000 kg, is about 200 pounds heavier than a 2000-lb ton.

Liquid / Space Volume. A liter holds a bit more than a quart. A liquid ounce (not the same as a weight ounce!!!) is about 30 milliliters or 30 cubic centimeters.

Temperature. The Celsius temperature scale runs from 0E to 100E, from water's freezing to boiling point, Fahrenheit 32E to 212E, a span of 100E compared to 180E. A Celsius degree is equal to almost two Fahrenheit degrees. With that knowledge, also knowing a couple of "crossover points" on the two scales helps to quickly convert one temperature to the other. The OE C - 32E F is one crossover point; room temperature, considered to be 25E C and 78E F, is another; body temperature is 38E C and 98.6E F. You just work up and down from a crossover point and use your 1-to-2 ratio conversion on the gap.

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PRECISION CONVERSIONS

Use the conversions on this page to make precise conversions back-and-forth from English to SI.

Temperature.

For readings on the temperature scales, use the following conversions, doing the stuff in the parentheses first.

For pure temperature changes, where the readings are not off the temperature scales:

1.8 X Celsius change = Fahrenheit change

.56 X Fahrenheit change = Celsius change

Length.

1 meter = 39.37 inches                             1 foot = 30.48 centimeters

1 centimeter = 0.3937 inches                     1 inch = 2.540 centimeters

1 kilometer = 0.6214 miles                         1 mile = 1.609 kilometers

Mass / Weight.

1 gram = 0.035 weight ounces                     1 weight ounce = 28.4 grams

1 kilogram = 2.20 pounds                            1 pound = 454 grams

Volume.

1 milliliter = 0.032 liquid ounce                  1 liquid ounce = 29.56 milliliters

1 liter = 1.06 quart                                        1 quart = 0.946 liter

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9.                                                                                 10.

How Different Units are Related.

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2.

3.

Conversions - See Table, Other Side.

Extra Credit - Show work for partial credit.

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2.

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Conversion Table

Remember, give numbers AND units!

 Object Measured Actual Measurement, English Units "Ballpark" Conversion to SI Units "Precise" Conversion to SI Units Actual Measurement, SI Units

Prefixes. How Many...

1. Meters in 25 kilometers?                                     2. Micrograms in 9 grams?

3. Milliliters in 37 liters?                                            4. Bytes in a gigabyte?

5. Milligrams in 3 kilograms?                                    6. Seconds in 17 nanoseconds?

7. Micrometers in 0.5 meters?                                  8. Centiliters in 45 liters?

9. Centiliters in 1.6 liters?                                         10. Micrograms in 34 kilograms?

How Different Units are Related. Show work for this part.

1. What is the mass or weight of a single milliliter of pure water?

2. How many SI calories does it take to raise one liter of water 6E Celsius?

3. An 1-meter deep inset bathtub measures a meter wide and two meters long inside. How much extra weight would the floor need to support if the tub were filled with water to the brim? Bonus Point - Also give answer in English units.

Conversions.

Use the objects listed below to fill in the table on the answer sheet. Everything but one object will be measured twice, once in English units and once in SI units. The conversions will use the English data and come up with SI figures - rough approximations in the "Ballpark" column and exact calculations in the "Precise" column.

Objects: Length of your own left pinky finger.

Temperature* of the room (don't use thermostat reading!).

Volume of baby juice jar.

Length of your own right forearm.

Mass of empty English measuring cup.

Mass of 2 cups of water, minus mass of cup.

Total length of the lab table, end-to-end.

Volume of 2 cups of water.

Temperature* of water from refrigerator.

Approximate distance from home to school (English only, don't actually measure)

* Make sure English & SI temperature readings are taken simultaneously!

Extra Credit. Show work for up to Two Points Each.

1. Water Analysis Readings can be taken in milligrams of material per liter of water or in part material per million parts water. If you had mg/L, how could you convert it to ppm?

2. How many SI calories would it take to bring a half-gallon of water from the refrigerator up to the lab's room temperature, as you measured them?

First Written 1988;  Last Update 2003;  Web Version 2003,  M. McDarby

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