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1018

microbes in a teaspoon of soil (108); of grains of sand on all the beaches of the Earth (maybe 1020); of living things on Earth (1029); of atoms in all the life on Earth (1041); of atomic nuclei in the Sun (1057); or of the number of elementary particles (electrons, protons, neutrons) in the entire Cosmos (1080). This doesn't mean you can picture a billion or a quintillion objects in your head—nobody can. But, with exponential notation, we can think about and calculate with such numbers. Pretty good for self-taught beings who started out with no possessions and who could number their fellows on their fingers and toes. Really big numbers are part and parcel of modern science; but I don't want to leave the impression that they were invented in our time.

Indian arithmetic has long been equal to large numbers. You can easily find references in Indian newspapers today to fines or expenditures of lakh or crore rupees. The key is: das =10; san = 100; hazar = 1,000; lakh = 105; crore = 107; arahb = 109; carahb = 10"; nie = 1013; padham = 1015; and sankh = 1017. Before their culture was annihilated by the Europeans, the Maya of ancient Mexico devised a world timescale that dwarfed the paltry few thousand years that the Europeans thought had passed since the creation of the world. Among the decaying monuments of Coba, in Quintana Roo, are inscriptions showing that the Maya were contemplating a Universe around 1029 years old. The Hindus held that the ? the Universe is 8.6 X 109

One 1 10° 1 second Thousand

1,000 103 17 minutes Million 1,000,000

106 12 days Billion 1,000,000,000 109 32

years Trillion 1,000,000,000,000 1012 32,000 years

(longer than there has been civilization on Earth) Quadrillion 1,000,000,000,000,000 1015 32 million years (longer than there have been humans on Earth) Quintillion 1,000,000,000,000,000,000 1018 32 billion years (more than the age of the Universe) Larger numbers are called a (1024), octillion (1027), nonillion

(1030), and decillion (1033).The Earth has a mass of 6 octillion grams.

present incarnation o

That scientific or exponential notation also is described by words. Thus, an electron is a femtometer (10~ m) across; yellow light has a wavelength of half a micrometer (0.5 |J.m); the human eye can barely see a bug a tenth of a millimeter (10~4 m) across; the Earth has a radius of 6,300 kilometers (6,300 km = 6.3 Mm); and a mountain might weigh 100 peta-grams (100 pg = 1017 g).

years old—almost right on the button. And the third century B.C. Sicilian mathematician Archimedes, in his book The Sand-Reckoner, estimated that it would take 1063 grains of sand to fill the Cosmos. On the really big questions, billions and billions were small change even then.

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