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This section illustrates several systems for naming large numbers, and shows how they can be extended past vigintillion . Traditional British usage assigned new names for each power of one million (the long scale ): 1,000,000 = 1 million; 1,000,0002 = 1 billion; 1,000,0003 = 1 trillion; and so on. It was adapted from French usage, and is ...
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 ...
A typical book can be printed with 10 6 zeros (around 400 pages with 50 lines per page and 50 zeros per line). Therefore, it requires 10 94 such books to print all the zeros of a googolplex (that is, printing a googol zeros).
In number theory, Skewes's number is any of several large numbers used by the South African mathematician Stanley Skewes as upper bounds for the smallest natural number for which. π x li x. where π is the prime-counting function and li is the logarithmic integral function. Skewes's number is much larger, but it is now known that there is a ...
The Riemann zeta function ζ ( s) is a function whose argument s may be any complex number other than 1, and whose values are also complex. It has zeros at the negative even integers; that is, ζ ( s ) = 0 when s is one of −2, −4, −6, .... These are called its trivial zeros. The zeta function is also zero for other values of s, which are ...
For whole numbers smaller than 1,000,000,000 (10 9 ), such as one thousand or one million, the two scales are identical. For larger numbers, starting with 10 9, the two systems differ. For identical names, the long scale proceeds by powers of one million, whereas the short scale proceeds by powers of one thousand.
Power of 10. Visualisation of powers of 10 from one to 1 trillion. A power of 10 is any of the integer powers of the number ten; in other words, ten multiplied by itself a certain number of times (when the power is a positive integer). By definition, the number one is a power (the zeroth power) of ten. The first few non-negative powers of ten are:
If it is the rough estimation, then only the first three non-zero digits are significant since the trailing zeros are neither reliable nor necessary; 45600 m can be expressed as 45.6 km or as 4.56 × 10 4 m in scientific notation, and neither expression requires the trailing zeros. An exact number has an infinite number of significant figures.