Orders of magnitude (numbers)

This list contains selected positive numbers in increasing order of magnitude, including counts of things, dimensionless quantities, 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: The difference between 3 and the next smallest fusible number is less than

1

/

(

2

↑

9

16

)

{\displaystyle 1/(2\uparrow ^{9}16)}

in Knuth's up-arrow notation.

Mathematics: 2−1541023937 ≈ 8.4489×10−463894430 is the difference between 3 and the next smallest tame fusible number as defined by Erickson et al. (2021).

Mathematics: 10−183800 is the approximate probability that a typing "monkey", or an English-illiterate typing robot, when placed in front of a typewriter with no spaces or punctuation, will type out William Shakespeare's play Hamlet on the first try.

Computing: 2−262378 ≈ 2.24800708647703657297018614776265182597360918266100276294348974547709294462×10−78984 is the smallest non-zero value that can be represented by an octuple-precision IEEE floating-point value.

Computing: 2−262142 ≈ 2.48242795146434978829932822291387172367768770607964686927095329791378756×10−78913 is the smallest positive normal number that can be represented by an octuple-precision IEEE floating-point value.

Computing: 1×10−6176 is the smallest non-zero value that can be represented by a quadruple-precision IEEE decimal floating-point value.

Computing: 1×10−6143 is the smallest positive normal number that can be represented by a quadruple-precision IEEE decimal floating-point value.