Orders of magnitude (numbers)

This list contains selected positive numbers in increasing order, including counts of things, dimensionless quantity and probabilities. Each number is given a name in the short scale, which is used in English-speaking countries, as well as a name in the long scale, which is used in some of the countries that do not have English as their national language.

Smaller than 10−100 (one googolth)

  • Mathematics – Writing: Approximately 10−183,800 is a rough first estimate of the probability that an immortal monkey, placed in front of a typewriter and given adequate food, breaks, and sleep while doing so, will type all the letters of Hamlet on the first try. This is the same as the average number of letters needed to be typed for Hamlet to be produced. However, taking punctuation, capitalization, and spacing into account, the actual probability is far less: around 10−360,783.
  • Computing: The number 1×10−6176 is equal to the smallest positive non-zero value that can be represented by a quadruple-precision IEEE decimal floating-point value.
  • Nanosecond

    A nanosecond (ns) is an SI unit of time equal to one billionth of a second (10−9 or 1/1,000,000,000 s). One nanosecond is to one second as one second is to 31.71 years.

    The word nanosecond is formed by the prefix nano and the unit second. Its symbol is ns.

    A nanosecond is equal to 1000 picoseconds or 11000 microsecond. Because the next SI unit is 1000 times larger, times of 10−8 and 10−7 seconds are typically expressed as tens or hundreds of nanoseconds.

    Times of this magnitude are commonly encountered in telecommunications, pulsed lasers and some areas of electronics.

    Light travels approximately 29.98 centimeters in 1 nanosecond. This is equivalent to 11.8 inches, leading to some to refer to a nanosecond as a light-foot. The earliest use of the term is by George Gamow. Another early reference commonly given is to Admiral Grace Hopper, who used to give out pieces of wire about a foot long to illustrate the eventual problem of building very high speed computers. If it takes light a nanosecond to go a foot (in a vacuum, slower in copper), then a computer built with parts connected by half this distance, 15 centimetres (5.9 in) of wire, would take at least a nanosecond to send data to a part and get a response. The solution, developed in Hopper's lifetime, was first the integrated circuit and later the multi-core processor.

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