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In mathematics, a rational number is a number that can be expressed as the quotient or fraction of two integers, a numerator p and a non-zero denominator q. [1] For example, is a rational number, as is every integer (for example, ). The set of all rational numbers, also referred to as " the rationals ", [2] the field of ...
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 .
The following list includes the continued fractions of some constants and is sorted by their representations. Continued fractions with more than 20 known terms have been truncated, with an ellipsis to show that they continue. Rational numbers have two continued fractions; the version in this list is the shorter one.
Duty cycle. A duty cycle or power cycle is the fraction of one period in which a signal or system is active. [1][2][3] Duty cycle is commonly expressed as a percentage or a ratio. A period is the time it takes for a signal to complete an on-and-off cycle. As a formula, a duty cycle (%) may be expressed as: Equally, a duty cycle (ratio) may be ...
A percentage point or percent point is the unit for the arithmetic difference between two percentages. For example, moving up from 40 percent to 44 percent is an increase of 4 percentage points (although it is a 10-percent increase in the quantity being measured, if the total amount remains the same). [ 1 ]
A unit fraction is a positive fraction with one as its numerator, 1/ n. It is the multiplicative inverse (reciprocal) of the denominator of the fraction, ...
The number e is a mathematical constant approximately equal to 2.71828 that is the base of the natural logarithm and exponential function.It is sometimes called Euler's number, after the Swiss mathematician Leonhard Euler, though this can invite confusion with Euler numbers, or with Euler's constant, a different constant typically denoted .
The fraction 1/17 also produces 0.05882353 when rounded to 8 digits. 2 1 + 6 2 + 4 3 + 6 4 + 7 5 + 9 6 + 8 7 = 2646798 {\displaystyle \,2^{1}+6^{2}+4^{3}+6^{4}+7^{5}+9^{6}+8^{7}=2646798} . The largest number with this pattern is 12157692622039623539 = 1 1 + 2 2 + 1 3 + … + 9 20 {\displaystyle \,12157692622039623539=1^{1}+2^{2}+1^{3}+\ldots +9 ...