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A simple fraction (also known as a common fraction or vulgar fraction) [n 1] is a rational number written as a/b or , where a and b are both integers. [9] As with other fractions, the denominator (b) cannot be zero. Examples include 1 / 2 , − 8 / 5 , −8 / 5 , and 8 / −5 .
Conversely the period of the repeating decimal of a fraction c / d will be (at most) the smallest number n such that 10 n − 1 is divisible by d. For example, the fraction 2 / 7 has d = 7, and the smallest k that makes 10 k − 1 divisible by 7 is k = 6, because 999999 = 7 × 142857. The period of the fraction 2 / 7 is ...
1/4 or 1 ⁄ 4 or ¼ may refer to: The calendar date January 4, in month-day format; The calendar date 1 April in day-month format; 1st Battalion, 4th Marines, an infantry battalion in the United States Marine Corps; A fraction of one fourth, one quarter, 25% or 0.25; 1/4 (single album), a single album by South Korean band Onewe
To say that the golden ratio is rational means that is a fraction / where and are integers. We may take n / m {\displaystyle n/m} to be in lowest terms and n {\displaystyle n} and m {\displaystyle m} to be positive.
A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. [1]
The fraction 99 / 70 (≈ 1.4142857) is sometimes used as a good rational approximation with a reasonably small denominator. Sequence A002193 in the On-Line Encyclopedia of Integer Sequences consists of the digits in the decimal expansion of the square root of 2, here truncated to 65 decimal places: [2]
Graph of the fractional part of real numbers. The fractional part or decimal part [1] of a non‐negative real number is the excess beyond that number's integer part.The latter is defined as the largest integer not greater than x, called floor of x or ⌊ ⌋.
Today, a more standard phrasing of Archimedes' proposition is that the partial sums of the series 1 + 1 / 4 + 1 / 16 + ⋯ are: + + + + = +. This form can be proved by multiplying both sides by 1 − 1 / 4 and observing that all but the first and the last of the terms on the left-hand side of the equation cancel in pairs.