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People also ask
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What is a rational approximation of a real number?
By a “good” rational approximation a/b to a real number α we mean that a/b is close to α, and a and b are relatively small. We define the best approximation to a real number α relative to n to be the rational number a/b closest to α satisfying 0 < b < n.
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What is the best rational approximation of √ 29?
Prime Factorisation Method The square root of 29 = √29 ≈ 5.385 (approx.)
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What is a rational approximation?
Rational Numbers: Rational numbers are numbers that can be written as fractions (and in turn, decimals). Rational Approximations: A rational approximation of an irrational number is a fraction or decimal that nearly equals the value of the irrational number.
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What makes a good approximation?
A 'Good Approximation' refers to a rational number that is close to a given real number, with relatively small numerator and denominator values. It is the best approximation to the real number within a specified range.
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What is a good rational approximation?
A rational number x/y is referred to as "the best approximation of the first kind" if c/d≠x/y and 0
|α−x/y|. -
What is a good approximation of pi?
Practical approximations Depending on the purpose of a calculation, π can be approximated by using fractions for ease of calculation. The most notable such approximations are 22⁄7 (relative error of about 4·10−4) and 355⁄113 (relative error of about 8·10−8).
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