Orders of magnitude (numbers)

Smaller than (one googolth)

• Mathematics – random selections: Approximately is a rough first estimate of the probability that a typing "monkey", or an English-illiterate typing robot, when placed in front of a typewriter, will type out William Shakespeare's play Hamlet as its first set of inputs, on the precondition it typed the needed number of characters. However, demanding correct punctuation, capitalization, and spacing, the probability falls to around 10^−360,783.
• Computing: 2.2 is approximately equal to the smallest non-zero value that can be represented by an octuple-precision IEEE floating-point value.
• Computing: 2.5 is approximately equal to the smallest positive normal number that can be represented by an octuple-precision IEEE floating-point value.
• Computing: 1 is equal to the smallest non-zero value that can be represented by a quadruple-precision IEEE decimal floating-point value.
• Computing: 1 is equal to the smallest positive normal number that can be represented by a quadruple-precision IEEE decimal floating-point value.
• Computing: 6.5 is approximately equal to the smallest non-zero value that can be represented by a quadruple-precision IEEE floating-point value.
• Computing: 3.6 is approximately equal to the smallest non-zero value that can be represented by an 80-bit x86 double-extended IEEE floating-point value.
• Computing: 3.4 is approximately equal to 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 equal to the smallest non-zero value that can be represented by a double-precision IEEE decimal floating-point value.
• Computing: 1 is equal to the smallest positive normal number that can be represented by a double-precision IEEE decimal floating-point value.
• Computing: 4.9 is approximately equal to the smallest non-zero value that can be represented by a double-precision IEEE floating-point value.
• Computing: 2.2 is approximately equal to the smallest positive normal number that can be represented by a double-precision IEEE floating-point value.
• Mathematics: 1.5 is approximately equal to the probability that in a randomly selected group of 365 people, all of them will have different birthdays.
• Computing: 1 is equal to 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: The chances of shuffling a standard 52-card deck in any specific order is around 1.24
• Computing: The number 1.4 is approximately equal to the smallest positive non-zero value that can be represented by a single-precision IEEE floating-point value.
• Computing: The number 1.2 is approximately equal to the smallest positive normal number that can be represented by a single-precision IEEE floating-point value.

  10⁻³⁰

• Mathematics: The probability in a game of bridge of all four players getting a complete suit each is approximately.

  10⁻²⁷

10⁻²⁴

10⁻²¹

• Mathematics: The probability of matching 20 numbers for 20 in a game of keno is approximately 2.83 × 10⁻¹⁹.
• Mathematics: The odds of a perfect bracket in the NCAA Division I men's basketball tournament are 1 in 2⁶³, approximately 1.08 × 10⁻¹⁹, if coin flips are used to predict the winners of the 63 matches.

  10⁻¹⁸

• Mathematics: The probability of rolling snake eyes 10 times in a row on a pair of fair dice is about.

  10⁻¹⁵

• Mathematics: The Ramanujan constant, is an almost integer, differing from the nearest integer by approximately.

  10⁻¹²

• Mathematics: The probability in a game of bridge of one player getting a complete suit is approximately .
• Biology: Human visual sensitivity to 1000 nm light is approximately of its peak sensitivity at 555 nm.

  10⁻⁹

• Mathematics – Lottery: The odds of winning the Grand Prize 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 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 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: The number 6 is approximately equal to 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 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

• Mathematics – Poker: The odds of being dealt a royal flush in poker are 649,739 to 1 against, for a probability of 1.5.
• Mathematics – Poker: The odds of being dealt a straight flush in poker are 72,192 to 1 against, for a probability of 1.4.
• Computing: The number 6.1 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 4,164 to 1 against, for a probability of 2.4.

  10⁻³

• 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.
• 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.
• Mathematics – Poker: The odds of being dealt a straight in poker are 253.8 to 1 against, for a probability of 4 × 10⁻³.
• Physics: ''α'' =, the fine-structure constant.

  10⁻²

• 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.
• 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.
• 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.
• Mathematics – Poker: The odds of being dealt two pair in poker are 21 to 1 against, for a probability of 0.048.

  10⁻¹

• 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 number with method.
• Mathematics – Poker: The odds of being dealt only one pair in poker are about 5 to 2 against, for a probability of 0.42.
• Mathematics – Poker: The odds of being dealt no pair in poker are nearly 1 to 2, for a probability of about 0.5.
• Mathematics: Natural logarithm of 2| ≈ 0.693147181

  10⁰

• 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.
• 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.
• Mathematics: 1 is the only natural number that is not prime or composite.
• Computing: 1.0000000000000000000000000000000001926 is 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.
• Mathematics: Cube root of 2| ≈, 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: Square root of 2| ≈, 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: Square root of 3| ≈, 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: Square root of 5| ≈ 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: ? ≈, 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 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.
• Literature: 9 circles of Hell in the Inferno by Dante Alighieri.
• Mathematics: 9 is the first odd number that is composite.