Metric System Fundamentals

International System (SI) of Measurements SI Prefixes

-1- Time Scale

Symbol Name Equivalent

ys Yoctosecond* = 10-24 second zs Zeptosecond* = 10-21 second as Attosecond* = 10-18 second fs Femtosecond = 10-15 second ps Picosecond = 10-12 second ns Nanosecond = 10-9 second ìs Microsecond = 10-6 second ms Millisecond = 10-3 second cs Centisecond* = 10-2 second ds Decisecond* = 10-1 second s Second = 1 second

Other Conversion Units

60 seconds = 1 minute 60 minutes = 1 hour 24 hours = 1 day 8,760 hours = 1 year 365 days = 1 year 10 years = 1 decade 100 years = 1 century 1,000 years = 1 millennium

* Not commonly used

-2- Dimensional Metric Scale

Symbol Name Equivalent

ym Yoctometer* = 10-24 meter zm Zeptometer* = 10-21 meter am Attometer* = 10-18 meter fm Femtometer* = 10-15 meter pm Picometer* = 10-12 meter Å Angstrom = 10-10 meter Å Angstrom = 10-4 micron nm Nanometer = 10-9 meter ìm Micrometer = 10-6 meter ì Micron = 1 micrometer mm Millimeter = 10-3 meter cm Centimeter = 10-2 meter dm Decimeter = 10-1 meter m Meter = 1 meter dam Decameter = 10 meters hm Hectometer = 102 meters km Kilometer = 103 meters * Not commonly used Other Conversion Units

km 1 Kilometer = 6.21 x 10-1 mile mile 1 Mile = 1.61 kilometers km 1 Kilometer = 1,094 yards km 1 Kilometer = 3,281 feet km 1 Kilometer = 6.68 x 10-9 astronomical units AU 1 Astronomical Unit = 1.49598 108 kilometers km 1 Kilometer = 1.057 x 10-13 light-years light-year 1 Light Year = 9.46 x 1012 kilometers light-year 1 Light Year = 6.3274 x 104 AU km 1 Kilometer = 3.24 x 10-14 parsecs parsec 1 Parsec = 3.0838 x 1013 kilometers parsec 1 Parsec = 2.06265 x 105 AU c Speed of Light = 3 x 1010 centimeters/second c Speed of Light = 3 x 108 meters/second c Speed of Light = 3 x 105 kilometers/second

-3- Mass Metric Scale

Symbol Name Equivalent

pg Picogram* = 10-12 gram ng Nanogram = 10-9 gram ìg Microgram = 10-6 gram mg Milligram = 10-3 gram cg Centigram = 10-2 gram dg Decigram = 10-1 gram g Gram = 1 gram kg Kilogram = 103 grams megag Megagrams* = 106 grams gigag Gigagrams* = 109 grams tonne Metric Ton = 106 grams tonne Metric Ton = 103 kilograms kilotonne Kilotonne = 106 kilograms, 103 tonnes megatonne Megatonne = 109 kilograms, 106 tonnes gigatonne Gigatonne = 1012 kilograms, 109 tonnes

* Not commonly used

Other Conversion Units

kg 1 Kilogram = 2.205 pounds kg 1 Kilogram = 35.27 ounces** g 1 Gram = 3.527 x 10-2 ounces** oz** 1 Ounce = 28.35 grams lb 1 Pound = 454 grams lb 1 Pound = 0.454 kilograms lb 1 Pound = 16 ounces** ton 1 Short Ton = 2,000 pounds ton 1 Short Ton = 907.18 kilograms

** Ounces of mass are called “ avoirdupois” ounces

-4- Volume Metric Scale

Symbol Name Equivalent

pl Picoliiter* = 10-12 liter nl Nanoliter* = 10-9 liter ìl Microliter = 10-6 liter ml Milliliter = 10-3 liter cl Centiliter = 10-2 liter, 10 ml dc Deciliter = 10-1 liter, 100 ml l Liter = 1 liter kl Kiloliter = 103 liters

* Not commonly used Other Conversion Units

l 1 Liter = 33.81 fluid ounces l 1 Liter = 1.057 quarts l 1 Liter = 2.113 pints l 1 Liter = 0.264 gallons l 1 Liter = 103 cubic centimeters ml 1 Milliliter = 1 cubic centimeter oz 1 Fluid Ounce = 29.57 cubic centimeters oz 1 Fluid Ounce = 29.57 milliliters oz 1 Fluid Ounce = 2.96 x 10-2 liters gal 1 Gallon** = 3.788 liters gal 1 Gallon** = 128 fluid ounces

** U.S. gallon

-5- Temperature Scales

Water Reference Points

Symbol Name Freezing Point Boiling Point

o C Degrees Celsius 0 o C 100 o C

o F Degrees Fahrenheit 32 o F 212 o F

K Kelvin 273 K 373 K

A temperature of “absolute zero” is 0 K, -273 o C, or -460 o F.

Kelvin Scale

Symbol Name Equivalent

pK Picokelvin* = 10-12 K nK Nanokelvin = 10-9 K ìK Microkelvin = 10-6 K mK Millikelvin = 10-3 K cK Centikelvin = 10-2 K dK Decikelvin = 10-1 K K Kelvin = 1 K

* The lowest temperature known to be recorded is 450 pK or 4.5 x 10-10 K (Science, September 12, 2003). This was accomplished by a combination of laser cooling and evaporative cooling.

Conversion Factors

o F to o C: o C = 5 (o F - 32) 9 o o o C to o F: F = 9 C + 32 5 o C to K: K = o C + 273; K to o C: o C = K - 273

o o F to K: K = 273 + 5 ( F - 32) 9 K to o F: o F = 1.8 (K-273) + 32

-6- Temperature Scale History Notes

Daniel Fahrenheit (1686-1736), a German physicist, developed the first widely used temperature scale in 1724. He used a bath of ice and ammonium chloride to determine the lowest temperature, which he set at 0 degrees. He thought that this mixture had the lowest melting point of anything then available. He set the 100- degree point at the temperature of the hottest day that summer and so the Fahrenheit scale was born.

Anders Celsius (1701-1744), a Swedish astronomer, developed his scale in 1741, but according to reports, he set 0 as the boiling point of water and 100 as the freezing point of water. After his death in 1744, the scale was reversed and established as the centigrade scale, which it was known as until the name was officially changed to Celsius in 1948 at an international conference. However, the centigrade scale was in wide use during that time and it took many years before the term degrees Celsius became widely used throughout the world. In fact, college textbooks from the 1950s used degrees centigrade. The use of the centigrade scale carried through at least until the 1970s, so many older scientists might still use the term degrees centigrade or simply degrees C.

William Thomson “Lord” Kelvin (1824-1907), an Irish-born mathematician and physicist, wrote a paper in 1848 on the need for a scale whereby “infinite cold” or “absolute zero” was the scale’s lowest point and represented the absence of all thermal energy. Kelvin used degree Celsius for its unit increment and calculated that absolute zero was equivalent to -273 °C on the air thermometers of the time. This absolute scale is known today as the Kelvin thermodynamic temperature scale. Kelvin’s value of “-273” was the reciprocal of 0.00366 - the accepted expansion coefficient of gas per degree Celsius relative to the ice point, giving a remarkable consistency to the currently accepted value. Unlike degrees Fahrenheit and degrees Celsius, the Kelvin is not referred to as a “degree,” nor is it typeset with a degree symbol. Instead, it is written K and not °K.

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