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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.
ten lakh 1,000,000,000: 10 9: one billion a thousand million: one milliard a thousand million: one hundred crore (one arab) 1,000,000,000,000: 10 12: one trillion a thousand billion: one billion a million million: one lakh crore (ten kharab) 1,000,000,000,000,000: 10 15: one quadrillion a thousand trillion: one billiard a thousand billion: ten ...
The name of a number 10 3n+3, where n is greater than or equal to 1000, is formed by concatenating the names of the numbers of the form 10 3m+3, where m represents each group of comma-separated digits of n, with each but the last "-illion" trimmed to "-illi-", or, in the case of m = 0, either "-nilli-" or "-nillion". [17]
Numbers from 100 up are more regular. There are numerals for 100, sau; 1,000, hazār; and successive multiples by 100 of 1000: lākh (lakh) 100,000 (10 5), karoṛ ...
Each of these words translates to the American English or post-1974 British English word billion (10 9 in the short scale). The term billion originally meant 10 12 when introduced. [7] In long scale countries, milliard was defined to its current value of 10 9, leaving billion at its original 10 12 value and so on for the larger numbers. [7]
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For example, the Panchavimsha Brahmana lists 10 9 as nikharva, 10 10 vâdava, 10 11 akṣiti, while Śâṅkhyâyana Śrauta Sûtra has 10 9 nikharva, 10 10 samudra, 10 11 salila, 10 12 antya, 10 13 ananta. Such lists of names for powers of ten are called daśaguṇottarra saṁjñâ. There area also analogous lists of Sanskrit names for ...
For example, class 5 is defined to include numbers between 10 10 10 10 6 and 10 10 10 10 10 6, which are numbers where X becomes humanly indistinguishable from X 2 [14] (taking iterated logarithms of such X yields indistinguishibility firstly between log(X) and 2log(X), secondly between log(log(X)) and 1+log(log(X)), and finally an extremely ...