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A simple fraction (also known as a common fraction or vulgar fraction, where vulgar is Latin for "common") 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 .
For example, 1 / 4 , 5 / 6 , and −101 / 100 are all irreducible fractions. On the other hand, 2 / 4 is reducible since it is equal in value to 1 / 2 , and the numerator of 1 / 2 is less than the numerator of 2 / 4 . A fraction that is reducible can be reduced by dividing both the numerator ...
The number π (/ p aɪ /; spelled out as "pi") is a mathematical constant that is the ratio of a circle's circumference to its diameter, approximately equal to 3.14159.The number π appears in many formulae across mathematics and physics.
A decimal separator is a symbol that separates the integer part from the fractional part of a number written in decimal form (e.g., "." in 12.45 ). Different countries officially designate different symbols for use as the separator.
In order to convert a rational number represented as a fraction into decimal form, one may use long division. For example, consider the rational number 5 / 74 : 0.0 675 74 ) 5.00000 4.44 560 518 420 370 500 etc. Observe that at each step we have a remainder; the successive remainders displayed above are 56, 42, 50.
In the 3rd century BCE, Archimedes proved the sharp inequalities 223 ⁄ 71 < π < 22 ⁄ 7, by means of regular 96-gons (accuracies of 2·10 −4 and 4·10 −4, respectively). [ 15 ] In the 2nd century CE, Ptolemy used the value 377 ⁄ 120 , the first known approximation accurate to three decimal places (accuracy 2·10 −5 ). [ 16 ]
This fraction may be derived by subtracting 1 from the reciprocal of the chances of winning; for any odds longer than "even money," this fraction will be an improper one. [3] [4] Odds of 4:1 ("four-to-one" or less commonly "four-to-one against ") would imply that the bettor stands to make a £400 profit on a £100 stake.
As an example, when using an unsigned 8-bit fixed-point format (which has 4 integer bits and 4 fractional bits), the highest representable integer value is 15, and the highest representable mixed value is 15.9375 (0xF.F or 1111.1111 b). If the desired real world values are in the range [0,160], they must be scaled to fit within this fixed-point ...