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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 .
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 radical sign √, denoting a square root, is equivalent to exponentiation to the power of 1 / 2 . The ± sign means the equation can be written with either a + or a – sign.
A continued fraction is a mathematical expression that can be written as a fraction with a denominator that is a sum that contains another simple or continued fraction. Depending on whether this iteration terminates with a simple fraction or not, the continued fraction is finite or infinite .
Irrational numbers can also be expressed as non-terminating continued fractions (which in some cases are periodic), and in many other ways. As a consequence of Cantor's proof that the real numbers are uncountable and the rationals countable, it follows that almost all real numbers are irrational. [3]
The nilradical is the radical of the zero ideal. A radical ideal is an ideal that equals its own radical. In a polynomial ring k [ x 1 , … , x n ] {\displaystyle k[x_{1},\ldots ,x_{n}]} over a field k , an ideal is radical if and only if it is the set of all polynomials that are zero on an affine algebraic set (this is a consequence of ...
The fraction (1.732 142 857...) can be used as a good approximation. Despite having a denominator of ...
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]