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 in Knuth's up-arrow notation. Mathematics: 2−1541023937 ≈ is the difference between 3 and the next smallest tame fusible number as defined by Erickson et al. (2021). Mathematics: 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 ≈ is the smallest non-zero value that can be represented by an octuple-precision IEEE floating-point value. Computing: 2−262142 ≈ is the smallest positive normal number that can be represented by an octuple-precision IEEE floating-point value. Computing: 1 is the smallest non-zero value that can be represented by a quadruple-precision IEEE decimal floating-point value. Computing: 1 is the smallest positive normal number that can be represented by a quadruple-precision IEEE decimal floating-point value. Computing: 2−16494 ≈ is the smallest non-zero value that can be represented by a quadruple-precision IEEE floating-point value. Computing: 2−16445 ≈ is the smallest non-zero value that can be represented by an 80-bit x86 double-extended IEEE floating-point value. Computing: 2−16382 ≈ 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 is the smallest non-zero value that can be represented by a double-precision IEEE decimal floating-point value. Computing: 1 is the smallest positive normal number that can be represented by a double-precision IEEE decimal floating-point value. Computing: 2−1074 ≈ is the smallest non-zero value that can be represented by a double-precision IEEE floating-point value. Computing: 2−1022 ≈ is the smallest positive normal number that can be represented by a double-precision IEEE floating-point value. Mathematics: ≈ 1.45 is the probability that in a randomly selected group of 365 people, all of them will have different birthdays. Computing: 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 is equal to the smallest positive normal number that can be represented by a single-precision IEEE decimal floating-point value. Mathematics: ≈ 1.24 is the probability of shuffling a standard 52-card deck in any specific order. Computing: 2−149 ≈ is the smallest positive non-zero value that can be represented by a single-precision IEEE floating-point value. Computing: 2−126 ≈ is the smallest positive normal number that can be represented by a single-precision IEEE floating-point value.

10−30 (; 1000−10; short scale: one nonillionth; long scale: one quintillionth)

ISO: quecto- (q) Mathematics: ≈ 4.47 is the approximate probability in a game of bridge of all four players getting a complete suit each.

10−27 (; 1000−9; short scale: one octillionth; long scale: one quadrilliardth)

ISO: ronto- (r)

10−24 (; 1000−8; short scale: one septillionth; long scale: one quadrillionth)

ISO: yocto- (y)

10−21 (; 1000−7; short scale: one sextillionth; long scale: one trilliardth)

ISO: zepto- (z) Mathematics: ≈ 2.83 is the probability of matching 20 numbers for 20 in a game of keno. Mathematics: 2−63 ≈ 1.08 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

(; 1000−6; short scale: one quintillionth; long scale: one trillionth)

ISO: atto- (a) Mathematics: 36−10 ≈ is the probability of rolling snake eyes 10 times in a row on a pair of fair dice.

10−15 (; 1000−5; short scale: one quadrillionth; long scale: one billiardth)

ISO: femto- (f) Mathematics: The Ramanujan constant, is an almost integer, differing from the nearest integer by approximately .

10−12 (; 1000−4; short scale: one trillionth; long scale: one billionth)

ISO: pico- (p) Mathematics: is the approximate probability in a game of bridge of one player getting a complete suit. Biology: Human visual sensitivity to 1000 nm light is approximately of its peak sensitivity at 555 nm.

10−9 (; 1000−3; short scale: one billionth; long scale: one milliardth)

ISO: nano- (n) Mathematics – Lottery: The odds of winning the Grand Prize (matching all 6 numbers) in the US Powerball lottery, with a single ticket, under the rules , are 292,201,338 to 1 against, for a probability of (). Mathematics – Lottery: The odds of winning the Grand Prize (matching all 6 numbers) in the Australian Powerball lottery, with a single ticket, under the rules , are 134,490,400 to 1 against, for a probability of (). Mathematics – Lottery: The odds of winning the Jackpot (matching the 6 main numbers) in the current 59-ball UK National Lottery Lotto, with a single ticket, under the rules , are 45,057,474 to 1 against, for a probability of (). Computing: 2−24 ≈ is the smallest positive non-zero value that can be represented by a half-precision IEEE floating-point value. Mathematics – Lottery: The odds of winning the Jackpot (matching the 6 main numbers) in the former 49-ball UK National Lottery, with a single ticket, were 13,983,815 to 1 against, for a probability of ().

10−6 (; 1000−2; long and short scales: one millionth)

ISO: micro- (μ)

+ Poker hands Hand Chance 1. Royal flush 2. Straight flush 0.0014% 3. Four of a kind 0.024% 4. Full house 0.14% 5. Flush 0.19% 6. Straight 0.59% 7. Three of a kind 2.1% 8. Two pairs 4.8% 9. One pair 42% 10. No pair 50% Mathematics – Poker: The odds of being dealt a royal flush in poker are approximately 649,739 to 1 against, for a probability of 1.5 (0.00015%). Mathematics – Poker: The odds of being dealt a straight flush (other than a royal flush) in poker are approximately 72,192 to 1 against, for a probability of 1.4 (0.0014%). Computing: 2−14 ≈ 6.104 is approximately equal to the smallest positive normal number that can be represented by a half-precision IEEE floating-point value. Mathematics – Poker: The odds of being dealt a four of a kind in poker are approximately 4,164 to 1 against, for a probability of 2.4 (0.024%).

10−3 (0.001; 1000−1; one thousandth)

ISO: milli- (m) Mathematics – Poker: The odds of being dealt a full house in poker are 693 to 1 against, for a probability of 1.4 × 10−3 (0.14%). Mathematics – Poker: The odds of being dealt a flush in poker are 507.8 to 1 against, for a probability of 1.9 × 10−3 (0.19%). Mathematics – Poker: The odds of being dealt a straight in poker are 253.8 to 1 against, for a probability of 4 × 10−3 (0.39%). Physics: α = is the fine-structure constant

10−2 (0.01; one hundredth)

ISO: centi- (c) Mathematics – Lottery: The odds of winning any prize in the UK National Lottery, with a single ticket, under the rules as of 2003, are 54 to 1 against, for a probability of about 0.018 (1.8%). Mathematics – Poker: The odds of being dealt a three of a kind in poker are 46 to 1 against, for a probability of 0.021 (2.1%). Mathematics – Lottery: The odds of winning any prize in the Powerball, with a single ticket, under the rules as of 2015, are 24.87 to 1 against, for a probability of 0.0402 (4.02%). Mathematics – Poker: The odds of being dealt two pair in poker are 21 to 1 against, for a probability of 0.048 (4.8%).

10−1 (0.1; one tenth)

ISO: deci- (d) Legal history: 10% was widespread as the tax raised for income or produce in the ancient and medieval period; see tithe. Mathematics: ≈ 0.333333333, which is the first repeating decimal with the form 1/n. Mathematics – Poker: The odds of being dealt only one pair in poker are about 5 to 2 against (2.37 to 1), for a probability of 0.42 (42%). Mathematics – Poker: The odds of being dealt no pair in poker are nearly 1 to 2, for a probability of 0.5 (50%). Mathematics: ≈ 0.693147181

100

(1; one) Demography: The population of Monowi, an incorporated village in Nebraska, United States, was one in 2010. Religion: One is the number of gods in Judaism, Christianity, and Islam (monotheistic religions). Computing – Unicode: One character is assigned to the Lisu Supplement Unicode block, the fewest of any public-use Unicode block as of Unicode 15.0 (2022). Mathematics: 1 is the only natural number (not including 0) that is not prime or composite. Computing: 1.00000000000000000000000000000000000000000000000000000000000000000000000906 is approximately equal to the smallest value greater than one that can be represented in the IEEE octuple-precision floating-point format. Computing: 1.0000000000000000000000000000000001926 is approximately equal to the smallest value greater than one that can be represented in the IEEE quadruple-precision floating-point format. Computing: 1.0000000000000002 is approximately equal to the smallest value greater than one that can be represented in the IEEE double precision floating-point format. Computing: 1.00000011920928955 is approximately equal to the smallest value greater than one that can be represented in the IEEE single precision floating-point format. Computing: 1.00097656 is approximately equal to the smallest value greater than one that can be represented in the IEEE half-precision floating-point format. Motorsport: 1.07 (107%) is the upper limit, on a dry track, for the ratio between the duration of a Formula One Grand Prix entrant's fastest qualifying lap and that of the polesitter's fastest qualifying lap, above which the entrant fails to qualify for the race unless specially permitted. Mathematics: ≈ , the length of a side of a cube with a volume of 2. Mathematics: If the Riemann hypothesis is true, Mills' constant is approximately 1.3063778838630806904686144926... . Mathematics: ≈ , the ratio of the diagonal of a square to its side length. Mathematics: ≈ 1.587 401 051 968 2, the length of a cube with a volume of 4. Mathematics: φ ≈ , the golden ratio. Mathematics: ≈ , the ratio of the diagonal of a unit cube. Mathematics: the number system understood by most computers, the binary system, uses 2 digits: 0 and 1. Mathematics: √4 = 2, the ratio of a diagonal of a unit tesseract. Mathematics: ≈ 2.236 067 9775, the correspondent to the diagonal of a rectangle whose side lengths are 1 and 2. Mathematics: + 1 ≈ , the silver ratio; the ratio of the smaller of the two quantities to the larger quantity is the same as the ratio of the larger quantity to the sum of the smaller quantity and twice the larger quantity. Mathematics: e ≈ , the base of the natural logarithm. Mathematics: the number system understood by ternary computers, the ternary system, uses 3 digits: 0, 1, and 2. Religion: Three persons of God in the Christian Trinity. Mathematics: π ≈ , the ratio of a circle's circumference to its diameter. Religion: the Four Noble Truths in Buddhism. Human scale: There are five digits on a human hand, and five toes on a human foot. Mathematics: 6 is the smallest perfect number. Mathematics: 𝜏 ≈ , the ratio of a circle's circumference to its radius. Biology: 7 ± 2, in cognitive science, George A. Miller's estimate of the number of objects that can be simultaneously held in human working memory. Music: 7 notes in a major or minor scale. Astronomy: 8 confirmed planets in the Solar System: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune. Biology – Spider anatomy: Eight jointed legs of a spider. Religion: the Noble Eightfold Path in Buddhism.