Time for Learning

Multiplication Table

Use the table below and follow these steps to find the answer to a multiplication problem. 1) Pick a number from the top row (in bold), let’s choose 6. 2) Pick another number, this time from the left column (also in bold), let’s choose 4. 3) From 4, move right until you find the box that lines up with the 6 in the top row. That box has 24 in it, this is the answer since 6 x 4 = 24.

× 0 1 2 3 4 5 6 7 8 9 10 11 12
0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 2 3 4 5 6 7 8 9 10 11 12
2 0 2 4 6 8 10 12 14 16 18 20 22 24
3 0 3 6 9 12 15 18 21 24 27 30 33 36
4 0 4 8 12 16 20 24 28 32 36 40 44 48
5 0 5 10 15 20 25 30 35 40 45 50 55 60
6 0 6 12 18 24 30 36 42 48 54 60 66 72
7 0 7 14 21 28 35 42 49 56 63 70 77 84
8 0 8 16 24 32 40 48 56 64 72 80 88 96
9 0 9 18 27 36 45 54 63 72 81 90 99 108
10 0 10 20 30 40 50 60 70 80 90 100 110 120
11 0 11 22 33 44 55 66 77 88 99 110 121 132
12 0 12 24 36 48 60 72 84 96 108 120 132 144

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Use this table to find the squares and square roots of numbers from 1 to 100.
You can also use this table to estimate the square roots of larger numbers.

  • For instance, if you want to find the square root of 2000, look in the middle column until you find the number that is closest to 2000. The number in the middle column that is closest to 2000 is 2,025.

  • Now look in at the number to the left of 2,025 to find its square root. The square root of 2,025 is 45.

  • Therefore, the approximate square root of 2,000 is 45.

To get a more exact number, you will have to use a calculator (44.721 is the more exact square root of 2,000).

number square square root
1 1 1.000
2 4 1.414
3 9 1.732
4 16 2.000
5 25 2.236
6 36 2.449
7 49 2.646
8 64 2.828
9 81 3.000
10 100 3.162
11 121 3.317
12 144 3.464
13 169 3.606
14 196 3.742
15 225 3.873
16 256 4.000
17 289 4.123
18 324 4.243
19 361 4.359
20 400 4.472
21 441 4.583
22 484 4.690
23 529 4.796
24 576 4.899
25 625 5.000
26 676 5.099
27 729 5.196
28 784 5.292
29 841 5.385
30 900 5.477
31 961 5.568
32 1,024 5.657
33 1,089 5.745
34 1,156 5.831
35 1,225 5.916
36 1,296 6.000
37 1,369 6.083
38 1,444 6.164
39 1,521 6.245
40 1,600 6.325
41 1,681 6.403
42 1,764 6.481
43 1,849 6.557
44 1,936 6.633
45 2,025 6.708
46 2,116 6.782
47 2,209 6.856
48 2,304 6.928
49 2,401 7.000
50 2,500 7.071
51 2,601 7.141
52 2,704 7.211
53 2,809 7.280
54 2,916 7.348
55 3,025 7.416
56 3,136 7.483
57 3,249 7.550
58 3,364 7.616
59 3,481 7.681
60 3,600 7.746
61 3,721 7.810
62 3,844 7.874
63 3,969 7.937
64 4,096 8.000
65 4,225 8.062
66 4,356 8.124
67 4,489 8.185
68 4,624 8.246
69 4,761 8.307
70 4,900 8.367
71 5,041 8.426
72 5,184 8.485
73 5,329 8.544
74 5,476 8.602
75 5,625 8.660
76 5,776 8.718
77 5,929 8.775
78 6,084 8.832
79 6,241 8.888
80 6,400 8.944
81 6,561 9.000
82 6,724 9.055
83 6,889 9.110
84 7,056 9.165
85 7,225 9.220
86 7,396 9.274
87 7,569 9.327
88 7,744 9.381
89 7,921 9.434
90 8,100 9.487
91 8,281 9.539
92 8,464 9.592
93 8,649 9.644
94 8,836 9.695
95 9,025 9.747
96 9,216 9.798
97 9,409 9.849
98 9,604 9.899
99 9,801 9.950
100 10,000 10.000
NOTE: Square roots in this table are rounded to the nearest thousandth.

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Would you like to pay for your purchase in camels or cocoa beans? Perhaps you'd like your change in shells. Throughout history, all kinds of things have been used as money. Precious metals have kept their popularity since they're easy to handle (unlike camels) and keep their value. Here is how cold cash is measured around the world.
Country Currency
Australia dollar
Brazil real
China yuan
Czech Republic koruna
Denmark krone
Ethiopia birr
France euro (formerly French franc)
Germany euro (formerly Deutsche mark)
Ghana cedi
Greece Euro (formerly drachma)
Haiti gourde
India rupee
Israel shekel
Italy Euro (formerly lira)
Japan yen
Jordan dinar
Laos kip
Malaysia ringgit
Mexico peso
Mongolia tugrik
Morocco dirham
The Netherlands Euro (formerly guilder)
Peru nuevo sol
Poland zloty
Portugal Euro (formerly escudo)
Russia ruble
Saudi Arabia riyal
South Africa rand
South Korea won
Spain Euro (formerly peseta)
Sweden krona
Thailand baht
United Kingdom pound sterling
United States dollar
Venezuela bolivar
Zambia kwacha

Fact Monster/Information Please® Database, © 2007 Pearson Education, Inc. All rights reserved.
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Adrenaline: (Isolation of) John Jacob Abel, U.S., 1897.
Aerosol can: Erik Rotheim, Norway, 1926.
Air brake: George Westinghouse, U.S., 1868.
Air conditioning: Willis Carrier, U.S., 1911.
Airship: (Non-rigid) Henri Giffard, France, 1852; (rigid) Ferdinand von Zeppelin, Germany, 1900.
Aluminium manufacture: (by electrolytic action) Charles M. Hall, U.S., 1866. Anatomy, human:
(De fabrica corporis humani, an illustrated systematic study of the human body) Andreas Vesalius, Belgium, 1543; (comparative: parts of an organism are correlated to the functioning whole) Georges Cuvier, France, 1799–1805.
Anesthetic: (first use of anesthetic—ether—on humans) Crawford W. Long, U.S., 1842.
Antibiotics: (first demonstration of antibiotic effect) Louis Pasteur, Jules-François Joubert, France, 1887; (discovery of penicillin, first modern antibiotic) Alexander Fleming, Scotland, 1928; (penicillin's infection-fighting properties) Howard FloreyErnst Chain, England, 1940.
Antiseptic: (surgery) Joseph Lister, England, 1867.
Antitoxin, diphtheria: Emil von Behring, Germany, 1890.
Appliances, electric: (fan) Schuyler Wheeler, U.S., 1882; (flatiron) Henry W. Seely, U.S., 1882; (stove) Hadaway, U.S., 1896; (washing machine) Alva Fisher, U.S., 1906.
Aqualung: Jacques-Yves Cousteau, Emile Gagnan, France, 1943.
Aspirin: Dr. Felix Hoffman, Germany, 1899.
Astronomical calculator: The Antikythera device, Greece, first century B.C.. Found off island of Antikythera in 1900.
Atom: (Nuclear model of) Ernest Rutherford, England, 1911.
Atomic structure: (formulated nuclear model of atom, Rutherford model) Ernest Rutherford, England, 1911; (proposed current concept of atomic structure, the Bohr model) Niels Bohr, Denmark, 1913.
Atomic theory: (ancient) LeucippusDemocritus, Greece, c. 500 B.C.; Lucretius, Rome c.100 B.C.; (modern) John Dalton, England, 1808.
Automobile: (first with internal combustion engine, 250 rpm) Karl Benz, Germany, 1885; (first with practical high-speed internal combustion engine, 900 rpm) Gottlieb Daimler, Germany, 1885; (first true automobile, not carriage with motor) René Panhard, Emile Lavassor, France, 1891; (carburettor, spray) Charles E. Duryea, U.S., 1892.
Autopilot: (for aircraft) Elmer A. Sperry, U.S., c.1910, first successful test, 1912, in a Curtiss flying boat.
Avogadro's law: (equal volumes of all gases at the same temperature and pressure contain equal number of molecules)Amedeo Avogadro, Italy, 1811.
Bacteria: Anton van Leeuwenhoek, The Netherlands, 1683.
Balloon, hot-air: Joseph and Jacques Montgolfier, France, 1783.
Barbed wire: (Most popular) Joseph E. Glidden, U.S., 1873.
Bar codes (computer-scanned binary signal code): (retail trade use) Monarch Marking, U.S. 1970; (industrial use) Plessey Telecommunications, England, 1970.
Barometer: Evangelista Torricelli, Italy, 1643.
Bicycle: Karl D. von Sauerbronn, Germany, 1816; (first modern model) James Starley, England, 1884.
Big Bang theory: (the universe originated with a huge explosion) George LeMaitre, Belgium, 1927; (modified LeMaitre theory labeled “Big Bang”) George A. Gamow, U.S., 1948; (cosmic microwave background radiation discovered, confirms theory) Arno A. Penzias and Robert W. Wilson, U.S., 1965.
Blood, circulation of: William Harvey, England, 1628.
Boyle's law: (Relation between pressure and volume in gases) Robert Boyle, Ireland, 1662.
Braille: Louis Braille, France, 1829.
Bridges: (Suspension, iron chains) James Finley, Pa., 1800; (wire suspension) Marc Seguin, Lyons, 1825; (truss) Ithiel Town, U.S., 1820.
Bullet: (Conical) Claude Minié, France, 1849.
Calculating machine: (Logarithms: made multiplying easier and thus calculators practical) John Napier, Scotland, 1614; (slide rule) William Oughtred, England, 1632; (digital calculator) Blaise Pascal, 1642; (multiplication machine)Gottfried Leibniz, Germany, 1671; (important 19th-century contributors to modern machine) Frank S. Baldwin, Jay R. Monroe, Dorr E. Felt, W. T. Ohdner, William Burroughs, all U.S.; (“analytical engine” design, included concepts of programming, taping) Charles Babbage, England, 1835.
Calculus: Isaac Newton, England, 1669; (differential calculus) Gottfried Leibniz, Germany, 1684.
Camera: (hand-held) George Eastman, U.S., 1888; (Polaroid Land) Edwin Land, U.S., 1948.
“Canals” of Mars: Giovanni Schiaparelli, Italy, 1877.
Carpet sweeper: Melville R. Bissell, U.S., 1876.
Car radio: William Lear, Elmer Wavering, U.S., 1929, manufactured by Galvin Manufacturing Co., “Motorola.”
Cells: (word used to describe microscopic examination of cork) Robert Hooke, England, 1665; (theory: cells are common structural and functional unit of all living organisms) Theodor SchwannMatthias Schleiden, 1838–1839.
Cement, Portland: Joseph Aspdin, England, 1824.
Chewing gum: (spruce-based) John Curtis, U.S., 1848; (chicle-based) Thomas Adams, U.S., 1870.
Cholera bacterium: Robert Koch, Germany, 1883.
Circuit, integrated: (theoretical) G.W.A. Dummer, England, 1952; (phase-shift oscillator) Jack S. Kilby, Texas Instruments, U.S., 1959.
Classification of plants: (first modern, based on comparative study of forms) Andrea Cesalpino, Italy, 1583; (classification of plants and animals by genera and species) Carolus Linnaeus, Sweden, 1737–1753.
Clock, pendulum: Christian Huygens, The Netherlands, 1656.
Coca-Cola: John Pemberton, U.S., 1886.
Combustion: (nature of) Antoine Lavoisier, France, 1777.
Compact disk: RCA, U.S., 1972.
Computers: (first design of analytical engine) Charles Babbage, 1830s; (ENIAC, Electronic Numerical Integrator and Calculator, first all-electronic, completed) John Presper Eckert, Jr., John Mauchly, U.S., 1945; (dedicated at University of Pennsylvania) 1946; (UNIVAC, Universal Automatic Computer, handled both numeric and alphabetic data) 1951; (personal computer) Steve Wozniak, U.S., 1976.
Concrete: (reinforced) Joseph Monier, France, 1877.
Condensed milk: Gail Borden, U.S., 1853.
Conditioned reflex: Ivan Pavlov, Russia, c.1910.
Conservation of electric charge: (the total electric charge of the universe or any closed system is constant) Benjamin Franklin, U.S., 1751–1754.
Contagion theory: (infectious diseases caused by living agent transmitted from person to person) Girolamo Fracastoro, Italy, 1546.
Continental drift theory: (geographer who pieced together continents into a single landmass on maps) Antonio Snider-Pellegrini, France, 1858; (first proposed in lecture) Frank Taylor, U.S. 1912; (first comprehensive detailed theory)Alfred Wegener, Germany, 1912.
Contraceptive, oral: Gregory Pincus, Min Chuch Chang, John Rock, Carl Djerassi, U.S., 1951.
Converter, Bessemer: William Kelly, U.S., 1851.
Cosmetics: Egypt, c. 4000 B.C.
Cosmic string theory: (first postulated) Thomas Kibble, UK, 1976.
Cotton gin: Eli Whitney, U.S., 1793.
Crossbow: China, c. 300 B.C.
Cyclotron: Ernest O. Lawrence, U.S., 1931.
Defibrillator: Dr. William Bennett Kouwenhoven, U.S., 1932; (implantable) M. Stephen Heilman, MD, Dr. Alois Langer, Morton Mower, MD, Michel Mirowski, MD, 1980.
Deuterium: (heavy hydrogen) Harold Urey, U.S., 1931.
Disease: (chemicals in treatment of) crusaded by Philippus Paracelsus, 1527–1541; (germ theory) Louis Pasteur, France, 1862–1877.
DNA: (deoxyribonucleic acid) Friedrich Meischer, Germany, 1869; (determination of double-helical structure) F. H. Crick, England and James D. Watson, U.S., 1953.
Dye: (aniline, start of synthetic dye industry) William H. Perkin, England, 1856.
Dynamite: Alfred Nobel, Sweden, 1867.
Electric cooking utensil: (first) patented by St. George Lane-Fox, England, 1874.
Electric generator (dynamo): (laboratory model) Michael Faraday, England, 1832; Joseph Henry, U.S., c.1832; (hand-driven model) Hippolyte Pixii, France, 1833; (alternating-current generator) Nikola Tesla, U.S., 1892.
Electric lamp: (arc lamp) Sir Humphrey Davy, England, 1801; (fluorescent lamp) A.E. Becquerel, France, 1867; (incandescent lamp) Sir Joseph Swann, England, Thomas A. Edison, U.S., contemporaneously, 1870s; (carbon arc street lamp) Charles F. Brush, U.S., 1879; (first widely marketed incandescent lamp) Thomas A. Edison, U.S., 1879; (mercury vapor lamp) Peter Cooper Hewitt, U.S., 1903; (neon lamp) Georges Claude, France, 1911; (tungsten filament) Irving Langmuir, U.S., 1915.
Electrocardiography: Demonstrated by Augustus Waller, Switzerland, 1887; (first practical device for recording activity of heart)Willem Einthoven, 1903, Netherlands.
Electromagnet: William Sturgeon, England, 1823.
Electron: Sir Joseph J. Thompson, England, 1897.
Electronic mail: Ray Tomlinson, U.S., 1972.
Elevator, passenger: (safety device permitting use by passengers) Elisha G. Otis, U.S., 1852; (elevator utilizing safety device) 1857.
E = mc2: (Equivalence of mass and energy) Albert Einstein, Switzerland, 1907.
Engine, internal combustion: No single inventor. Fundamental theory established by Sadi Carnot, France, 1824; (two-stroke) Etienne Lenoir, France, 1860; (ideal operating cycle for four-stroke) Alphonse Beau de Roche, France, 1862; (operating four-stroke) Nikolaus Otto, Germany, 1876; (diesel) Rudolf Diesel, Germany, 1892; (rotary)Felix Wankel, Germany, 1956.
Evolution: (Organic) Jean-Baptiste Lamarck, France, 1809; (by natural selection) Charles Darwin, England, 1859.
Exclusion principle:
(no two electrons in an atom can occupy the same energy level) Wolfgang Pauli, Germany, 1925.
Expanding universe theory: (First proposed) George LeMaitre, Belgium, 1927; (discovered first direct evidence that the universe is expanding) Edwin P. Hubble, U.S., 1929; (Hubble constant: a measure of the rate at which the universe is expanding) Edwin P. Hubble, U.S., 1929.
Falling bodies, law of: Galileo Galilei, Italy, 1590.
Fermentation: (Microorganisms as cause of) Louis Pasteur, France, c.1860.
Fiber optics: Narinder Kapany, England, 1955.
Fibers, man-made: (Nitrocellulose fibers treated to change flammable nitrocellulose to harmless cellulose, precursor of rayon) Sir Joseph Swann, England, 1883; (rayon) Count Hilaire de Chardonnet, France, 1889; (Celanese) Henry and Camille Dreyfuss, U.S., England, 1921; (research on polyesters and polyamides, basis for modern man-made fibers) U.S., England, Germany, 1930s; (nylon) Wallace H. Carothers, U.S., 1935.
Frozen food: Clarence Birdseye, U.S., 1924.
Gene transfer: (Recombinant DNA organism) Herbert Boyer, Stanley Cohen, U.S., 1973; (human) Steven Rosenberg, R. Michael Blaese, W. French Anderson, U.S., 1989.
Geometry, elements of: Euclid, Alexandria, Egypt, c. 300 B.C.; (analytic) René Descartes, France; and Pierre de Fermat, Switzerland, 1637.
Gravitation, law of: Sir Isaac Newton, England, c.1665 (published 1687).
Gunpowder: China, c.700.
Gyrocompass: Elmer A. Sperry, U.S., 1905.
Gyroscope: Jean Léon Foucault, France, 1852.
Halley's Comet: Edmund Halley, England, 1705.
Heart implanted in human, permanent artificial: Dr. Robert Jarvik, U.S., 1982.
Heart, temporary artificial: Willem Kolff, Netherlands, U.S., 1957.
Helicopter: (double rotor) Heinrich Focke, Germany, 1936; (single rotor) Igor Sikorsky, U.S., 1939.
Helium first observed on sun: Sir Joseph Lockyer, England, 1868.
Heredity, laws of: Gregor Mendel, Austria, 1865.
Holograph: Dennis Gabor, England, 1947.
Home videotape systems (VCR): (Betamax) Sony, Japan, 1975; (VHS) Matsushita, Japan, 1975.
Ice age theory: Louis Agassiz, Swiss-American, 1840.
Induction, electric: Joseph Henry, U.S., 1828.
Insulin: (first isolated) Sir Frederick G. Banting and Charles H. Best, Canada, 1921; (discovery first published) Banting and Best, 1922; (Nobel Prize awarded for purification for use in humans) John Macleod and Banting, 1923; (first synthesized), China, 1966.
Intelligence testing: Alfred Binet, Theodore Simon, France, 1905.
Interferon: Alick Isaacs, England, Jean Lindemann, Switzerland, 1957.
Isotopes: (concept of) Frederick Soddy, England, 1912; (stable isotopes) J. J. Thompson, England, 1913; (existence demonstrated by mass spectrography) Francis W. Aston, England, 1919.
Jet propulsion: (Engine) Sir Frank Whittle, England, Hans von Ohain, Germany, 1936; (aircraft) Heinkel He 178, 1939.
Kinetic theory of gases: (Molecules of a gas are in a state of rapid motion) Daniel Bernoulli, Switzerland, 1738.
Laser: (Theoretical work on) Charles H. TownesArthur L. Schawlow, U.S., N. BasovA. Prokhorov, U.S.S.R., 1958; (first working model) T. H. Maiman, U.S., 1960.
Lawn mower: Edwin Budding, John Ferrabee, England, 1830–1831.
LCD (liquid crystal display): Hoffmann-La Roche, Switzerland, 1970.
Lens, bifocal: Benjamin Franklin, U.S., c.1760.
Leyden jar: (prototype electrical condenser) Canon E. G. von Kleist of Kamin, Pomerania, 1745; independently evolved by Cunaeus and P. van Musschenbroek, University of Leyden, Holland, 1746, from where name originated.
Light, nature of: (wave theory) Christian Huygens, The Netherlands, 1678; (electromagnetic theory) James Clerk Maxwell, England, 1873.
Light, speed of: (theory that light has finite velocity) Olaus Roemer, Denmark, 1675.
Lightning rod: Benjamin Franklin, U.S., 1752.
Lock, cylinder: Linus Yale, U.S., 1851.
Locomotive: (steam powered) Richard Trevithick, England, 1804; (first practical, due to multiple-fire-tube boiler) George Stephenson, England, 1829; (largest steam-powered) Union Pacific's “Big Boy,” U.S., 1941.
Loom: (horizontal, two-beamed) Egypt, c. 4400 B.C.; (Jacquard drawloom, pattern controlled by punch cards) Jacques de Vaucanson, France, 1745, Joseph-Marie Jacquard, 1801; (flying shuttle) John Kay, England, 1733; (power-driven loom) Edmund Cartwright, England, 1785.
Machine gun: (Hand-cranked multibarrel) Richard J. Gatling, U.S., 1862; (practical single barrel, belt-fed) Hiram S. Maxim, Anglo-American, 1884.
Magnet, Earth is: William Gilbert, England, 1600.
Match: (Phosphorus) François Derosne, France, 1816; (friction) Charles Sauria, France, 1831; (safety) J. E. Lundstrom, Sweden, 1855.
Measles vaccine: John F. Enders, Thomas Peebles, U.S., 1953.
Metric system: Revolutionary government of France, 1790–1801.
Microphone: Charles Wheatstone, England, 1827.
Microscope: (Compound) Zacharias Janssen, The Netherlands, 1590; (electron) Vladimir Zworykin et al., U.S., Canada, Germany, 1932–1939.
Microwave oven: Percy Spencer, U.S., 1947.
Motion, laws of: Isaac Newton, England, 1687.
Motion pictures:Thomas A. Edison, U.S., 1893.
Motion pictures, sound: Product of various inventions. First picture with synchronized musical score: Don Juan, 1926; with spoken dialogue: The Jazz Singer, 1927; both Warner Bros.
Motor, electric: Michael Faraday, England, 1822; (alternating-current) Nikola Tesla, U.S., 1892.
Motorcycle: (Motor tricycle) Edward Butler, England, 1884; (gasoline-engine motorcycle) Gottlieb Daimler, Germany, 1885.
Moving assembly line: Henry Ford, U.S., 1913.
Neptune: (Discovery of) Johann Galle, Germany, 1846.
Neptunium: (First transuranic element, synthesis of) Edward M. McMillan, Philip H. Abelson, U.S., 1940.
Neutron: James Chadwick, England, 1932.
Neutron-induced radiation: Enrico Fermi et al., Italy, 1934.
Nitroglycerin: Ascanio Sobrero, Italy, 1846.
Nuclear fission: Otto Hahn, Fritz Stresemann, Germany, 1938.
Nuclear reactor: Enrico Fermi, Italy, et al., 1942.
Ohm's law: (Relationship between strength of electric current, electromotive force, and circuit resistance) Georg S. Ohm, Germany, 1827.
Oil well: Edwin L. Drake, U.S., 1859.
Oxygen: (Isolation of) Joseph Priestley, England, 1774; Karl Scheele, Sweden, 1773.
Ozone: Christian Schönbein, Germany, 1839.
Pacemaker: (Internal) Clarence W. Lillehie, Earl Bakk, U.S., 1957.
Paper: China, c.100 A.D.
Parachute: Louis S. Lenormand, France, 1783.
Pen: (Fountain) Lewis E. Waterman, U.S., 1884; (ball-point, for marking on rough surfaces) John H. Loud, U.S., 1888; (ball-point, for handwriting) Lazlo Biro, Argentina, 1944.
Periodic law: (That properties of elements are functions of their atomic weights) Dmitri Mendeleev, Russia, 1869.
Periodic table: (Arrangement of chemical elements based on periodic law) Dmitri Mendeleev, Russia, 1869.
Phonograph: Thomas A. Edison, U.S., 1877.
Photography: (First paper negative, first photograph, on metal) Joseph Nicéphore Niepce, France, 1816–1827; (discovery of fixative powers of hyposulfite of soda) Sir John Herschel, England, 1819; (first direct positive image on silver plate, the daguerreotype) Louis Daguerre, based on work with Niepce, France, 1839; (first paper negative from which a number of positive prints could be made) William Talbot, England, 1841. Work of these four men, taken together, forms basis for all modern photography. (First colour images) Alexandre Becquerel, Claude Niepce de Saint-Victor, France, 1848–1860; (commercial colour film with three emulsion layers, Kodachrome) U.S., 1935.
Photovoltaic effect: (light falling on certain materials can produce electricity) Edmund Becquerel, France, 1839.
Piano: (Hammerklavier) Bartolommeo Cristofori, Italy, 1709; (pianoforte with sustaining and damper pedals) John Broadwood, England, 1873.
Planetary motion, laws of: Johannes Kepler, Germany, 1609, 1619.
Plant respiration and photosynthesis: Jan Ingenhousz, Holland, 1779.
Plastics: (first material, nitrocellulose softened by vegetable oil, camphor, precursor to Celluloid) Alexander Parkes, England, 1855; (Celluloid, involving recognition of vital effect of camphor) John W. Hyatt, U.S., 1869; (Bakelite, first completely synthetic plastic) Leo H. Baekeland, U.S., 1910; (theoretical background of macromolecules and process of polymerization on which modern plastics industry rests) Hermann Staudinger, Germany, 1922; (polypropylene and low-pressure method for producing high-density polyethylene) Robert Banks, Paul Hogan, U.S., 1958.
Plate tectonics: Alfred Wegener, Germany, 1912–1915.
Plow, forked: Mesopotamia, before 3000 B.C.
Plutonium, synthesis of: Glenn T. SeaborgEdwin M. McMillan, Arthur C. Wahl, Joseph W. Kennedy, U.S., 1941.
Polio, vaccine: (Experimentally safe dead-virus vaccine) Jonas E. Salk, U.S., 1952; (effective large-scale field trials) 1954; (officially approved) 1955; (safe oral live-virus vaccine developed) Albert B. Sabin, U.S., 1954; (available in the U.S.) 1960.
Positron: Carl D. Anderson, U.S., 1932.
Pressure cooker: (early version) Denis Papin, France, 1679.
Printing: (block) Japan, c.700; (movable type) Korea, c.1400, Johann Gutenberg, Germany, c.1450; (lithography, offset) Aloys Senefelder, Germany, 1796; (rotary press) Richard Hoe, U.S., 1844; (linotype) Ottmar Mergenthaler, U.S., 1884.
Probability theory: René Descartes, France, and Pierre de Fermat, Switzerland, 1654.
Proton: Ernest Rutherford, England, 1919.
Prozac: (Antidepressant fluoxetine) Bryan B. Malloy, Scotland, and Klaus K. Schmiegel, U.S., 1972; (released for use in U.S.) Eli Lilly & Company, 1987.
Psychoanalysis: Sigmund Freud, Austria, c.1904.
Pulsars: Antony Hewish and Jocelyn Bell Burnel, England, 1967.
Quantum theory: (general) Max Planck, Germany, 1900; (sub-atomic) Niels Bohr, Denmark, 1913; (quantum mechanics)Werner HeisenbergErwin Schrödinger, Germany, 1925.
Quarks: Jerome FriedmanHenry KendallRichard Taylor, U.S., 1967.
Quasars: Marten Schmidt, U.S., 1963.
Rabies immunization: Louis Pasteur, France, 1885.
Radar: (limited to one-mile range) Christian Hulsmeyer, Germany, 1904; (pulse modulation, used for measuring height of ionosphere) Gregory Breit, Merle Tuve, U.S., 1925; (first practical radar—radio detection and ranging) Sir Robert Watson-Watt, Scotland, 1934–1935.
Radio: (Electromagnetism, theory of) James Clerk Maxwell, England, 1873; (spark coil, generator of electromagnetic waves) Heinrich Hertz, Germany, 1886; (first practical system of wireless telegraphy)Guglielmo Marconi, Italy, 1895; (first long-distance telegraphic radio signal sent across the Atlantic) Marconi, 1901; (vacuum electron tube, basis for radio telephony) Sir John Fleming, England, 1904; (triode amplifying tube) Lee de Forest, U.S., 1906; (regenerative circuit, allowing long-distance sound reception)Edwin H. Armstrong, U.S., 1912; (frequency modulation—FM) Edwin H. Armstrong, U.S., 1933.
Radioactivity: (X-rays) Wilhelm K. Roentgen, Germany, 1895; (radioactivity of uranium) Henri Becquerel, France, 1896; (radioactive elements, radium and polonium in uranium ore) Marie Sklodowska-CuriePierre Curie, France, 1898; (classification of alpha and beta particle radiation) Pierre Curie, France, 1900; (gamma radiation) Paul-Ulrich Villard, France, 1900.
Radiocarbon dating, carbon-14 method: (Discovered) Willard F. Libby, U.S., 1947; (first demonstrated) U.S., 1950.
Radio signals, extraterrestrial: first known radio noise signals were received by U.S. engineer, Karl Jansky, originating from the Galactic Center, 1931.
Radio waves: (Cosmic sources, led to radio astronomy) Karl Jansky, U.S., 1932.
Razor: (safety, successfully marketed) King Gillette, U.S., 1901; (electric) Jacob Schick, U.S., 1928, 1931.
Reaper: Cyrus McCormick, U.S., 1834.
Refrigerator: Alexander Twining, U.S., James Harrison, Australia, 1850; (first with a compressor device) the Domelse, Chicago, U.S., 1913.
Refrigerator ship: (first) the Frigorifique, cooling unit designed by Charles Teller, France, 1877.
Relativity: (special and general theories of) Albert Einstein, Switzerland, Germany, U.S., 1905–1953.
Revolver: Samuel Colt, U.S., 1835.
Richter scale: Charles F. Richter, U.S., 1935.
Rifle: (muzzle-loaded) Italy, Germany, c.1475; (breech-loaded) England, France, Germany, U.S., c.1866; (bolt-action) Paul von Mauser, Germany, 1889; (automatic) John Browning, U.S., 1918.
Rocket: (liquid-fueled) Robert Goddard, U.S., 1926.
Roller bearing: (Wooden for cartwheel) Germany or France, c.100 B.C.
Rotation of Earth: Jean Bernard Foucault, France, 1851.
Royal Observatory, Greenwich: established in 1675 by Charles II of England; John Flamsteed first Astronomer Royal.
Rubber: (vulcanization process) Charles Goodyear, U.S., 1839.
Saccharin: Constantine Fuhlberg, Ira Remsen, U.S., 1879.
Safety pin: Walter Hunt, U.S., 1849.
Saturn, ring around: Christian Huygens, The Netherlands, 1659.
“Scotch” tape:
Richard Drew, U.S., 1929.
Screw propeller: Sir Francis P. Smith, England, 1836; John Ericsson, England, worked independently of and simultaneously with Smith, 1837.
Seat belt: (three point) Nils Bohlin, Sweden, 1962.
Seismograph: (first accurate) John Milne, England, 1880.
Sewing machine: Elias Howe, U.S., 1846; (continuous stitch) Isaac Singer, U.S., 1851.
Solar energy: First realistic application of solar energy using parabolic solar reflector to drive caloric engine on steam boiler, John Ericsson, U.S., 1860s.
Solar system, universe: (Sun-centered universe) Nicolaus Copernicus, Warsaw, 1543; (establishment of planetary orbits as elliptical) Johannes Kepler, Germany, 1609; (infinity of universe) Giordano Bruno, Italian monk, 1584.
Spectrum: (heterogeneity of light) Sir Isaac Newton, England, 1665–1666.
Spectrum analysis: Gustav KirchhoffRobert Bunsen, Germany, 1859.
Spermatozoa: Anton van Leeuwenhoek, The Netherlands, 1683.
Spinning: (spinning wheel) India, introduced to Europe in Middle Ages; (Saxony wheel, continuous spinning of wool or cotton yarn) England, c.1500–1600; (spinning jenny) James Hargreaves, England, 1764; (spinning frame) Sir Richard Arkwright, England, 1769; (spinning mule, completed mechanization of spinning, permitting production of yarn to keep up with demands of modern looms) Samuel Crompton, England, 1779.
Star catalog: (first modern) Tycho Brahe, Denmark, 1572.
Steam engine: (first commercial version based on principles of French physicist Denis PapinThomas Savery, England, 1639; (atmospheric steam engine) Thomas Newcomen, England, 1705; (steam engine for pumping water from collieries) Savery, Newcomen, 1725; (modern condensing, double acting) James Watt, England, 1782; (high-pressure) Oliver Evans, U.S., 1804.
Steamship: Claude de Jouffroy d'Abbans, France, 1783; James Rumsey, U.S., 1787; John Fitch, U.S., 1790; (high-pressure) Oliver Evans, U.S., 1804. All preceded Robert Fulton, U.S., 1807, credited with launching first commercially successful steamship.
Stethoscope: René Laënnec, France, 1819.
Sulfa drugs: (parent compound, para-aminobenzenesulfanomide) Paul Gelmo, Austria, 1908; (antibacterial activity)Gerhard Domagk, Germany, 1935.
Superconductivity: (theory) John BardeenLeon Cooper, John Scheiffer, U.S., 1957.
Symbolic logic: George Boule, 1854; (modern) Bertrand RussellAlfred North Whitehead, England, 1910–1913.
Tank, military: Sir Ernest Swinton, England, 1914.
Tape recorder: (magnetic steel tape) Valdemar Poulsen, Denmark, 1899.
Teflon: DuPont, U.S., 1943.
Telegraph: Samuel F. B. Morse, U.S., 1837.
Telephone: Alexander Graham Bell, U.S., 1876.
Telescope: Hans Lippershey, The Netherlands, 1608; (astronomical) Galileo Galilei, Italy, 1609; (reflecting) Isaac Newton, England, 1668.
Television: (Iconoscope–T.V. camera table) Vladimir Zworykin, U.S., 1923, and also kinescope (cathode ray tube) 1928; (mechanical disk-scanning method) successfully demonstrated by J.L. Baird, Scotland, C.F. Jenkins, U.S., 1926; (first all-electric television image) Philo T. Farnsworth, U.S., 1927; (colour, mechanical disk) Baird, 1928; (colour, compatible with black and white) George Valensi, France, 1938; (colour, sequential rotating filter) Peter Goldmark, U.S., first introduced, 1951; (colour, compatible with black and white) commercially introduced in U.S., National Television Systems Committee, 1953.
Thermodynamics: (first law: energy cannot be created or destroyed, only converted from one form to another) Julius von Mayer, Germany, 1842; James Joule, England, 1843; (second law: heat cannot of itself pass from a colder to a warmer body) Rudolph Claudius, Germany, 1850; (third law: the entropy of ordered solids reaches zero at the absolute zero of temperature) Walter Nernst, Germany, 1918.
Thermometer: (open-column) Galileo Galilei, c.1593; (clinical) Santorio Santorio, Padua, c.1615; (mercury, also Fahrenheit scale) Gabriel D. Fahrenheit, Germany, 1714; (centigrade scale) Anders Celsius, Sweden, 1742; (absolute-temperature, or Kelvin, scale) William Thompson, Lord Kelvin, England, 1848.
Tire, pneumatic: Robert W. Thompson, England, 1845; (bicycle tire) John B. Dunlop, Northern Ireland, 1888.
Toilet, flush:
Product of Minoan civilization, Crete, c. 2000 B.C. Alleged invention by “Thomas Crapper” is untrue.
Tractor: Benjamin Holt, U.S., 1900.
Transformer, electric: William Stanley, U.S., 1885.
Transistor: John BardeenWalter H. BrattainWilliam B. Shockley, U.S., 1947.
Tuberculosis bacterium: Robert Koch, Germany, 1882.
Typewriter: Christopher Sholes, Carlos Glidden, U.S., 1867.
Uncertainty principle: (that position and velocity of an object cannot both be measured exactly, at the same time) Werner Heisenberg, Germany, 1927.
Uranus: (first planet discovered in recorded history) William Herschel, England, 1781.
Vaccination: Edward Jenner, England, 1796.
Vacuum cleaner: (manually operated) Ives W. McGaffey, U.S., 1869; (electric) Hubert C. Booth, England, 1901; (upright) J. Murray Spangler, U.S., 1907.
Van Allen (radiation) Belt: (around Earth) James Van Allen, U.S., 1958.
Video disk: Philips Co., The Netherlands, 1972.
Vitamins: (hypothesis of disease deficiency) Sir F. G. HopkinsCasimir Funk, England, 1912; (vitamin A) Elmer V. McCollum, M. Davis, U.S., 1912–1914; (vitamin B) McCollum, U.S., 1915–1916; (thiamin, B1) Casimir Funk, England, 1912; (riboflavin, B2) D. T. Smith, E. G. Hendrick, U.S., 1926; (niacin) Conrad Elvehjem, U.S., 1937; (B6) Paul Gyorgy, U.S., 1934; (vitamin C) C. A. Hoist, T. Froelich, Norway, 1912; (vitamin D) McCollum, U.S., 1922; (folic acid) Lucy Wills, England, 1933.
Voltaic pile: (forerunner of modern battery, first source of continuous electric current) Alessandro Volta, Italy, 1800.
Wallpaper: Europe, 16th and 17th century.
Wassermann test: (for syphilis) August von Wassermann, Germany, 1906.
Wheel: (cart, solid wood) Mesopotamia, c.3800–3600 B.C.
Windmill: Persia, c.600.
World Wide Web: (developed while working at CERN) Tim Berners-Lee, England, 1989; (development of Mosaic browser makes WWW available for general use) Marc Andreeson, U.S., 1993.
Xerography: Chester Carlson, U.S., 1938.
Yellow Fever: (transmission of) Walter Reed U.S., 1900.
Zero: India, c. 600; (absolute zero temperature, cessation of all molecular energy) William Thompson, Lord Kelvin, England, 1848.
Zipper: W. L. Judson, U.S., 1891.

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The factorial of a number is the product of all the whole numbers, except zero, that are less than or equal to that number. For example, to find the factorial of 7 you would multiply together all the whole numbers, except zero, that are less than or equal to 7. Like this:
7 x 6 x 5 x 4 x 3 x 2 x 1 = 5,040

The factorial of a number is shown by putting an exclamation point after that number. So, 7! is a way of writing “the factorial of 7” (or “7 factorial”).
Here are some factorials:
1! = 1 = 1
2! = 2 x 1 = 2
3! = 3 x 2 x 1 = 6
4! = 4 x 3 x 2 x 1 = 24
5! = 5 x 4 x 3 x 2 x 1 = 120
6! = 6 x 5 x 4 x 3 x 2 x 1 = 720
7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5,040
8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40,320
9! = 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 362,880
10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 3,628,800
11! = 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 39,916,800
12! = 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 479,001,600

Factorials are useful. They can show how many different ways there are to order or arrange a set of things. For example, if you have 5 books on a shelf, and want to know how many different ways there are to order or arrange them, simply find the factorial of 5:
5! = 5 x 4 x 3 x 2 x 1 = 120
This shows that you can arrange 5 books 120 different ways.
Here's a bit of trivia: mathematicians have decided that the factorial of zero, or 0!, is 1. Why? Because you can arrange a set of nothing, an empty set, in just one way—as nothing, an empty set.

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Common multiples are multiples that two numbers have in common. These can be useful when working with fractions and ratios.
Example:
What are some common multiples of 2 and 3?
  Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24...
  Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27...
Common multiples of 2 and 3 include 6, 12, 18, and 24.
Example:
What are some common multiples of 25 and 30?
  Multiples of 25: 25, 50, 75, 100, 125, 150, 175, 200, 225, 250, 275, 300, 325...
  Multiples of 30: 30, 60, 90, 120, 150, 180, 210, 240, 270, 300, 330...
Common multiples of 25 and 30 include 150 and 300.
The lowest common multiple or least common multiple is the lowest multiple two numbers have in common.
There are two ways of finding the lowest common multiple of two numbers.

Method 1: Listing Multiples

The first way to find the lowest common multiple is to do what we did above: write out a list of the lowest multiples of each number, and look for the lowest multiple both numbers have in common.
Example:
What is the lowest common multiple of 2 and 3?
  Multiples of 2: 2, 4, 6, 8...
  Multiples of 3: 3, 6, 9...
The lowest common multiple of 2 and 3 is 6.
Example:
What is the lowest common multiple of 25 and 30?
Multiples of 25: 25, 50, 75, 100, 125, 150, 175...
Multiples of 30: 30, 60, 90, 120, 150, 180...
The lowest common multiple of 25 and 30 is 150.

Method 2: Factors

The other way to find the lowest common multiple is to list the prime factors for each number. Remove the prime factors both numbers have in common. Multiply one of the numbers by the remaining prime factors of the other number. The result will be the lowest common multiple.
Example:
What is the lowest common multiple of 25 and 30?
  The prime factors of 25 are 5 x 5.
  The prime factors of 30 are 2 x 3 x 5.
  Remove the 5 that 25 and 30 have in common as a prime factor.
  Multiply 25 by the remaining prime factors of 30.
  25 x 2 x 3 = 150.
The lowest common multiple of 25 and 30 is 150.
You'll get the same results no matter which number you work with:
Example:
What is the lowest common multiple of 25 and 30?
  The prime factors of 25 are 5 x 5.
  The prime factors of 30 are 2 x 3 x 5.
  Remove the 5 that 25 and 30 have in common as a prime factor.
  Multiply 30 by the remaining prime factors of 25.
  30 x 5 = 150.
The lowest common multiple of 25 and 30 is 150.

Another Example

Example:
What is the lowest common multiple of 42 and 48?
  The prime factors of 42 are 2 x 3 x 7.
  The prime factors of 48 are 2 x 2 x 2 x 2 x 3.
  Remove the 2 x 3 that 42 and 48 have in common as prime factors.
  Multiply 48 by the remaining prime factors of 42.
  48 x 7 = 336.
The lowest common multiple of 42 and 48 is 336.

What if they have no prime factors in common?

Example:
What is the lowest common multiple of 44 and 45?
  The prime factors of 44 are 2 x 2 x 11.
  The prime factors of 45 are 3 x 3 x 5.
  44 and 45 have no prime factors in common.
Either:
  Multiply 44 by the remaining prime factors of 45.
  44 x 3 x 3 x 5 = 1980.
Or:
  Multiply 45 by the remaining prime factors of 44.
  45 x 2 x 2 x 11 = 1980.
Or:
  44 x 45 = 1980.
The lowest common multiple of 44 and 45 is 1980.
As that last example illustrates, if two numbers have no prime factors in common, the lowest common multiple will be equal to the product of the two numbers.

Treat primes as prime factors

If one number is prime, you can treat it as its own prime factor.
Example:
What is the lowest common multiple of 7 and 30?
  7 is a prime number.
  The prime factors of 30 are 2 x 3 x 5.
  7 and 30 have no prime factors in common.
  7 x 30 = 210.
The lowest common multiple of 7 and 30 is 210.
Example:
What is the lowest common multiple of 2 and 3?
  2 is a prime number.
  3 is a prime number.
  2 and 3 have no prime factors in common.
  2 x 3 = 6.
The lowest common multiple of 2 and 3 is 6.
Example:
What is the lowest common multiple of 3 and 30?
  3 is a prime number.
  The prime factors of 30 are 2 x 3 x 5.
  Remove the 3 that 3 and 30 have in common as a prime factor.
Either:
  Multiply 3 by the remaining prime factors of 30.
  3 x 2 x 5 = 30
or:
  You would normally multiply 30 by the remaining prime factors of 3, but there are no remaining prime factors.
The lowest common multiple is 30.

Prime results

As you can see from the above, there are two scenarios if at least one number is prime:
  • If one number is prime, and the other number's prime factors include that prime number, the lowest common multiple will be equal to the non-prime number.
  • If one number is prime, and the other number's prime factors do not include that prime number, the lowest common multiple will be equal to the product of the two numbers.
(The second scenario also includes cases where both numbers are prime.)
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If your friend has one-quarter of a pie, and she gives you half, how much of the pie do you have? Or, to put it another way, what's half of one-quarter? Or, to put it into mathematical notation:
1/2 x 1/4 = ?
To get the answer, multiply the numerators (the top parts) and denominators (the bottom parts) separately.
In this case, first we multiply the numerators:
1 x 1 = 1
Next we multiply the denominators:
2 x 4 = 8
The answer has a numerator of 1 and a denominator of 8. In other words:
1/2 x 1/4 = 1 x 1/2 x 4 = 1/8
You have one-eighth of the pie.

Another Example

Let's try another.
2/9 x 3/4 = ?
First we multiply the numerators:
2 x 3 = 6
Next we multiply the denominators:
9 x 4 = 36
The answer has a numerator of 6 and a denominator of 36. In other words:
2/9 x 3/4 = 2 x 3/9 x 4 = 6/36
This can be further reduced:
6 ÷ 6/36 ÷ 6 = 1/6
(See Reducing Fractions.)

Multiplying Mixed Numbers

To multiply two mixed numbers, or a mixed number and a fraction, first convert each mixed number to a fraction. Then multiply the fractions.
What is 21/3 x 1/4 = ?
First we write 21/3 as a fraction:
21/3 = 7/3
Then we multiply the fractions.
7/3 x 1/4 = ?
First we multiply the numerators:
7 x 1 = 7
Next we multiply the denominators:
3 x 4 = 12
The answer has a numerator of 7 and a denominator of 12. In other words:
21/3 x 1/4 = 7 x 1/3 x 4 = 7/12

Reference:
http://www.factmonster.com/ipka/A0933458.html

If your friend has half a pie, how many quarter-pies are in that half? Or, to put this into mathematical notation:
1/2 ÷ 1/4 = ?
To get the answer, flip the divisor (the second fraction) over, and then multiply the fractions. (Or, to put it another way, multiply the dividend [the first fraction] by the reciprocal of the divisor [the second fraction].)
In this case, that makes the problem:
1/2 x 4/1 = ?
We begin by multiplying the numerators:
1 x 4 = 4
And then we multiply the denominators:
2 x 1 = 2
The answer has a numerator of 4 and a denominator of 2. In other words:
1 x 4/2 x 1 =4/2
This fraction can be reduced to lowest terms:
4 ÷ 2/2 ÷ 2 =2/1 = 2
There are 2 quarter-pies in a half-pie.

Another Example

Let's try another:
4/5 ÷ 6/7 = ?
We flip the divisor over, and change the division sign to a multiplication sign:
4/5 x 7/6 = ?
We multiply the numerators:
4 x 7 = 28
And we multiply the denominators:
5 x 6 = 30
The answer has a numerator of 28 and a denominator of 30. In other words:
4 x 7/5 x 6 =28/30
We can reduce this fraction by dividing the numerator and denominator by 2:
28 ÷ 2/30 ÷ 2 = 14/15

Mixed Numbers

Let's try one more, this time with a mixed number:
21/4 ÷ 2/3 = ?
First we change the mixed number to an improper fraction:
9/4 ÷ 2/3 = ?
Next we flip the divisor over and change the division sign to a multiplication sign:
9/4 x 3/2 = ?
We multiply the numerators:
9 x 3 = 27
And we multiply the denominators:
4 x 2 = 8
The answer has a numerator of 27 and a denominator of 8. In other words:
9 x 3/4 x 2 =27/8
Finally, we turn the result—an improper fraction—into a mixed number.
27/8 = 33/8 =

Reference:
http://www.factmonster.com/ipka/A0933464.html

CIRCUMFERENCE

Circle:
C = πd, in which π is 3.1416 and d the diameter.

AREA

Triangle:
A = (ab)/2 , in which a is the base and b the height.
Square:
A = a2, in which a is one of the sides.
Rectangle:
A = ab, in which a is the base and b the height.
Trapezoid:
A = (h(a + b))/2, in which h is the height, a the longer parallel side, and b the shorter.
Regular pentagon:
A = 1.720a2, in which a is one of the sides.
Regular hexagon:
A = 2.598a2, in which a is one of the sides.
Regular octagon:
A = 4.828a2, in which a is one of the sides.
Circle:
A = πr2, in which π is 3.1416 and r the radius.

VOLUME

Cube:
V = a3, in which a is one of the edges.
Rectangular prism:
V = abc, in which a is the length, b is the width, and c the depth.
Pyramid:
V = (Ah)/3, in which A is the area of the base and h the height.
Cylinder:
V = πr2h, in which π is 3.1416, r the radius of the base, and h the height.
Cone:
V = (πr2h)/3, in which π is 3.1416, r theradius of the base, and h the height.
Sphere:
V = (4πr3)/3, in which π is 3.1416 and r the radius.
 

TEMPERATURE SCALES

Degrees Fahrenheit to Degrees Celsius:
TC = 5/9 (TF – 32)
Degrees Celsius to Degrees Fahrenheit:
TF = 9/5 TC + 32
Degrees Celsius to Kelvins:
TK = TC + 273.15
 

MISCELLANEOUS

Distance in feet traveled by falling body:
d = 16t2, in which t is the time in seconds.
Speed of sound in feet per second through any given temperature of air:
take the square root of (273 + t), in which t is the temperature Centigrade, multiply it by 1087, and divide the result by 16.52.
Cost in cents of operation of electrical device:
C = (Wtc)/1000, in which W is the number of watts,t the time in hours, and c the cost in cents per kilowatt-hour.
Conversion of matter into energy (Einstein's Theorem):
E = mc2, in which E is the energy in ergs, m the mass of the matter in grams, and c the speed of light in centimeters per second: (c2 = 9 × 1020)


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Elements

Element Symbol Atomic Number Atomic Weight1 Melting Point (Degrees Celsius) Boiling Point (Degrees Celsius)
actinium Ac 89 (227) 1050. 3200. ±300
aluminum Al 13 26.98154 660.37 2467.
americium Am 95 (243) 1172. 2600.
antimony Sb 51 121.760 630.74 1750.
argon Ar 18 39.948 - 189.2 - 185.7
arsenic As 33 74.92160 817. (at 28 atmospheres) 613. (sublimates)
astatine At 85 (210) 302. (est.) 337. (est.)
           
barium Ba 56 137.327 725. 1640.
berkelium Bk 97 (247) 1050. 2590.
beryllium Be 4 9.01218 1278. ±5 2970.
bismuth Bi 83 208.98040 271.3 1560. ±5
bohrium Bh 107 (270)
boron B 5 [10.806; 10.821] 2300. 2550. (sublimates)
bromine Br 35 79.904 - 7.2 58.78
           
cadmium Cd 48 112.411 320.9 765.
calcium Ca 20 40.078 839. ±2 1484.
californium Cf 98 (251) 900. 1470.
carbon C 6 [12.0096; 12.0116] ∼3550. 4827.
cerium Ce 58 140.116 799. 3426.
cesium Cs 55 132.90545 28.40 669.3
chlorine Cl 17 [35.446; 35.457] - 100.98 - 34.6
chromium Cr 24 51.9961 1857. ±20 2672.
cobalt Co 27 58.9332 1495. 2870.
copernicium Cn 112 (285)
copper Cu 29 63.546 1083.4 ±0.2 2567.
curium Cm 96 (247) 1340. ±40 3110.
           
darmstadtium Ds 110 (281)
dubnium Db 105 (268)
dysprosium Dy 66 162.500 1412. 2562.
           
einsteinium Es 99 (252) 857.
erbium Er 68 167.259 1529. 2863.
europium Eu 63 151.964 822. 1597.
           
fermium Fm 100 (257) 1527.
flerovium Fl 114 (289)
fluorine F 9 18.9984 - 219.62 - 188.14
francium Fr 87 (223) (27) (est.) (677) (est.)
           
gadolinium Gd 64 157.25 1313. ±1 3266.
gallium Ga 31 69.723 29.78 2403.
germanium Ge 32 72.63 937.4 2830.
gold Au 79 196.96657 1064.43 2808.
           
hafnium Hf 72 178.49 2227. ±20 4602.
hassium Hs 108 (277)
helium He 2 4.0026 < - 272.2 - 268.934
holmium Ho 67 164.93032 1474. 2425.
hydrogen H 1 [1.00784; 1.00811] - 259.14 - 252.87
           
indium In 49 114.818 156.61 2080.
iodine I 53 126.90447 113.5 184.35
iridium Ir 77 192.217 2410. 4130.
iron Fe 26 55.845 1535. 2750.
           
krypton Kr 36 83.798 - 156.6 - 152.30 ±0.10
           
lanthanum La 57 138.90547 921. 3457.
lawrencium Lr 103 (262) 1627.
lead Pb 82 207.2 327.502 1740.
lithium Li 3 [6.938; 6.997] 180.54 1342.
livermorium Lv 116 (292)
lutetium Lu 71 174.9668 1663. 3395.
           
magnesium Mg 12 24.3050 648.8 ±0.5 1090.
manganese Mn 25 54.93805 1244. ±3 1962.
meitnerium Mt 109 (276)
mendelevium Md 101 (258) 827.
mercury Hg 80 200.59 - 38.842 356.58
molybdenum Mo 42 95.96 2617. 4612.
           
neodymium Nd 60 144.242 1021. 3068.
neon Ne 10 20.1797 - 248.67 - 246.048
neptunium Np 93 (237) 640. ±1 3902. (est.)
nickel Ni 28 58.6934 1453. 2732.
niobium Nb 41 92.90638 2468. ±10 4742.
nitrogen N 7 [14.00643; 14.00728] - 209.86 - 195.8
nobelium No 102 (259) 827.
           
osmium Os 76 190.23 3045. ±30 5027. ±100
oxygen O 8 [15.99903; 15.99977] - 218.4 - 182.962
           
palladium Pd 46 106.42 1554. 2970.
phosphorus P 15 30.97376 44.1 (white) 280. (white)
platinum Pt 78 195.084 1772. 3827. ±100
plutonium Pu 94 (244) 641. 3232.
polonium Po 84 (209) 254. 962.
potassium K 19 39.0983 63.25 760.
praseodymium Pr 59 140.90765 931. 3512.
promethium Pm 61 (145) 1042 3000. (est.)
protactinium Pa 91 231.03588 <1600. 4026.
           
radium Ra 88 (226) 700. 1140.
radon Rn 86 (222) - 71. - 61.8
rhenium Re 75 186.207 3180. 5627. (est.)
rhodium Rh 45 102.90550 1966. ±3 3727. ±100
roentgenium Rg 111 (280)
rubidium Rb 37 85.4678 38.89 686.
ruthenium Ru 44 101.07 2310. 3900.
rutherfordium Rf 104 (265)
           
samarium Sm 62 150.36 1072. ±5 1791.
scandium Sc 21 44.95591 1541. 2831.
seaborgium Sg 106 (271)
selenium Se 34 78.96 217. 684.9 ±1.0
silicon Si 14 [28.084; 28.086] 1410. 2355.
silver Ag 47 107.8682 961.93 2212.
sodium Na 11 22.98977 97.81 ±0.03 882.9
strontium Sr 38 87.62 269. 1384.
sulfur S 16 [32.059; 32.076] 112.8 444.674
           
tantalum Ta 73 180.94788 2996. 5425. ±100
technetium Tc 43 (98) 2200. 4877.
tellurium Te 52 127.60 449.5 ±0.3 989.8 ±3.8
terbium Tb 65 158.92535 1356. 3123.
thallium Tl 81 [204.382; 204.385] 303.5 1457. ±10
thorium Th 90 232.03806 1750. ∼4790.
thulium Tm 69 168.93421 1545. ±15 1947.
tin Sn 50 118.710 231.9681 2270.
titanium Ti 22 47.867 1660. ±10 3287.
tungsten W 74 183.84 3410. ±20 5660.
           
ununoctium Uuo 118 (294)
ununpentium Uup 115 (288)
ununseptium Uus 117 (294)
ununtrium Uut 113 (284)
uranium U 92 238.02891 1132.3 ±0.8 3818.
           
vanadium V 23 50.9415 1890. ±10 3380.
           
xenon Xe 54 131.293 - 111.9 - 107.1 ±3
           
ytterbium Yb 70 173.054 819. 1194.
yttrium Y 39 88.90585 1522. ±8 3338.
           
zinc Zn 30 65.38 419.58 907.
zirconium Zr 40 91.224 1852. ±2 4377.
Footer 1) Parentheses indicate most stable isotope; brackets enclose lower and upper bounds of weight variation. Reference: http://www.factmonster.com/encyclopedia/science/elements-table.html

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