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)} . 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. Computing: 2−16494 ≈ 6.4751751194380251109244389582276466×10−4966 is the smallest non-zero value that can be represented by a quadruple-precision IEEE floating-point value. Computing: 2−16445 ≈ 3.6451995318824746025×10−4951 is the smallest non-zero value that can be represented by an 80-bit x86 double-extended IEEE floating-point value. Computing: 2−16382 ≈ 3.3621031431120935062626778173217526×10−4932 is the smallest positive normal number that can be represented by a quadruple-precision IEEE floating-point value and an 80-bit x86 double-extended IEEE floating-point value. Computing: 1×10−398 is the smallest non-zero value that can be represented by a double-precision IEEE decimal floating-point value. Computing: 1×10−383 is the smallest positive normal number that can be represented by a double-precision IEEE decimal floating-point value. Computing: 2−1074 ≈ 4.9406564584124654×10−324 is the smallest non-zero value that can be represented by a double-precision IEEE floating-point value. Computing: 2−1022 ≈ 2.2250738585072014×10−308 is the smallest positive normal number that can be represented by a double-precision IEEE floating-point value. Mathematics: 365 ! / 365 365 {\displaystyle 365!/365^{365}} ≈ 1.45×10−157 is the probability that in a randomly selected group of 365 people, all of them will have different birthdays. Computing: 1×10−101 is the smallest non-zero value that can be represented by a single-precision IEEE decimal floating-point value.
10−100 to 10−30
Computing: 1×10−95 is equal to the smallest positive normal number that can be represented by a single-precision IEEE decimal floating-point value. Mathematics: 1/52! ≈ 1.24×10−68 is the probability of shuffling a standard 52-card deck in any specific order. Computing: 2−149 ≈ 1.4012985×10−45 is the smallest positive non-zero value that can be represented by a single-precision IEEE floating-point value. Computing: 2−126 ≈ 1.1754944×10−38 is the smallest positive normal number that can be represented by a single-precision IEEE floating-point value.
10−30 (0.000000000000000000000000000001; 1000−10; short scale: one nonillionth; long scale: one quintillionth) ISO: quecto- (q)
Mathematics: 4 ! × ( 13 ! ) 4 / 52 ! {\displaystyle 4!\times (13!)^{4}/52!} ≈ 4.47×10−28 is the approximate probability in a game of bridge of all four players getting a complete suit each.
10−27 (0.000000000000000000000000001; 1000−9; short scale: one octillionth; long scale: one quadrilliardth) ISO: ronto- (r)
10−24 (0.000000000000000000000001; 1000−8; short scale: one septillionth; long scale: one quadrillionth) ISO: yocto- (y)
10−21 (0.000000000000000000001; 1000−7; short scale: one sextillionth; long scale: one trilliardth) ISO: zepto- (z)
Mathematics: 1 / ( 80 20 ) {\displaystyle 1/{\binom {80}{20}}} ≈ 2.83×10−19 is the probability of matching 20 numbers for 20 in a game of keno. Mathematics: 2−63 ≈ 1.08×10−19 is the odds of a perfect bracket in the NCAA Division I men's basketball tournament if coin flips of 50/50 are used to predict the winners of the 63 matches.
10−18
(0.000000000000000001; 1000−6; short scale: one quintillionth; long scale: one trillionth) ISO: atto- (a)
Mathematics: 36−10 ≈ 2.74×10−16 is the probability of rolling snake eyes 10 times in a row on a pair of fair dice.
10−15 (0.000000000000001; 1000−5; short scale: one quadrillionth; long scale: one billiardth) ISO: femto- (f)
Mathematics: The Ramanujan constant, e π 163 = 262 537 412 640 768 743.999 999 999 999 25 … , {\displaystyle e^{\pi {\sqrt {163}}}=262\,537\,412\,640\,768\,743.999\,999\,999\,999\,25\ldots ,} is an almost integer, differing from the nearest integer by approximately 7.5×10−13.
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