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Chuquet's book contains a passage in which he shows a large number marked off into groups of six digits, with the comment: Ou qui veult le premier point peult signiffier million Le second point byllion Le tiers point tryllion Le quart quadrillion Le cinq e quyllion Le six e sixlion Le sept. e septyllion Le huyt e ottyllion Le neuf e nonyllion ...
For powers of ten less than 9 (one, ten, hundred, thousand and million) the short and long scales are identical, but for larger powers of ten, the two systems differ in confusing ways. For identical names, the long scale grows by multiples of one million (10 6), whereas the short scale grows by multiples of one thousand (10 3).
I.e., if a number x is too large for a representation () the power tower can be made one higher, replacing x by log 10 x, or find x from the lower-tower representation of the log 10 of the whole number. If the power tower would contain one or more numbers different from 10, the two approaches would lead to different results, corresponding to ...
For higher powers of ten, naming diverges. The Indian system uses names for every second power of ten: lakh (10 5), crore (10 7), arab (10 9), kharab (10 11), etc. In the two Western systems, long and short scales, there are names for every third power of ten. The short scale uses million (10 6), billion (10 9), trillion (10 12), etc.
Kasner used it to illustrate the difference between an unimaginably large number and infinity, and in this role it is sometimes used in teaching mathematics. To put in perspective the size of a googol, the mass of an electron, just under 10 −30 kg, can be compared to the mass of the visible universe, estimated at between 10 50 and 10 60 kg. [ 5 ]
Mathematics: The probability of matching 20 numbers for 20 in a game of keno is approximately 2.83 × 10 −19. Mathematics: The odds of a perfect bracket in the NCAA Division I men's basketball tournament are 1 in 2 63, approximately 1.08 × 10 −19, if coin flips are used to predict the winners of the 63 matches. [6]
In fact, his monthly PayPal statement showed a negative balance of more than $92 quadrillion, which would have made him more than 5,500 times more indebted than the United States government.
If values differ by two orders of magnitude, they differ by a factor of about 100. Two numbers of the same order of magnitude have roughly the same scale: the larger value is less than ten times the smaller value. The growing amounts of Internet data have led to addition of new SI prefixes over time, most recently in 2022. [6]