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Note the logarithmic scale markings on each of the axes, and that the log x and log y axes (where the logarithms are 0) are where x and y themselves are 1. On the number line, the distance between two points is the unit length if and only if the difference of the represented numbers equals 1. Other choices are possible.
For a vertical line, this is 1 : 0, a kind of division by zero. In another interpretation, the quotient Q {\displaystyle Q} represents the ratio N : D . {\displaystyle N:D.} [ 6 ] For example, a cake recipe might call for ten cups of flour and two cups of sugar, a ratio of 10 : 2 {\displaystyle 10:2} or, proportionally, 5 : 1. {\displaystyle 5:1.}
In decimal numbers greater than 1 (such as 3.75), the fractional part of the number is expressed by the digits to the right of the separator (with a value of 0.75 in this case). 3.75 can be written either as an improper fraction, 375 / 100 , or as a mixed number, 3 + 75 / 100 .
Quaternary: The base-four numeral system with 0, 1, 2, and 3 as digits. Hexadecimal : Base 16, widely used by computer system designers and programmers, as it provides a more human-friendly representation of binary-coded values.
[0; 4, 4, 8, 16, 18, 5, 1, 1, 1, 1, 7, 1, 1, 6, 2, 9, 58, 1, 3, 4, …] [OEIS 100] Computed up to 1 011 597 392 terms by E. Weisstein. He also noted that while the Champernowne constant continued fraction contains sporadic large terms, the continued fraction of the Copeland–Erdős Constant do not exhibit this property. [Mw 85]
The geometric series on the real line. In mathematics, the infinite series 1 / 2 + 1 / 4 + 1 / 8 + 1 / 16 + ··· is an elementary example of a geometric series that converges absolutely. The sum of the series is 1. In summation notation, this may be expressed as
1 ⁄ 7: 0.142... Vulgar Fraction One Seventh 2150 8528 ⅑ 1 ⁄ 9: 0.111... Vulgar Fraction One Ninth 2151 8529 ⅒ 1 ⁄ 10: 0.1 Vulgar Fraction One Tenth 2152 8530 ⅓ 1 ⁄ 3: 0.333... Vulgar Fraction One Third 2153 8531 ⅔ 2 ⁄ 3: 0.666... Vulgar Fraction Two Thirds 2154 8532 ⅕ 1 ⁄ 5: 0.2 Vulgar Fraction One Fifth 2155 8533 ⅖ 2 ...
where f (2k−1) is the (2k − 1)th derivative of f and B 2k is the (2k)th Bernoulli number: B 2 = 1 / 6 , B 4 = − + 1 / 30 , and so on. Setting f ( x ) = x , the first derivative of f is 1, and every other term vanishes, so [ 15 ]