Same is the case for rational numbers. A fraction like "one/two" can be written as $0.5$ in decimals (as a finite expression), but the same can't be written as a finite decimal in ternary. …

The definitions of rational numbers are somewhat confusing for me. The definition of rational numbers on wikipedia and most other sites is: In mathematics, a rational number is any …

Therefore every rational number is represented by a decimal that either terminates or repeats. Formal proof attempt: Claim: if a number is rational, then it's decimal expansion either …

In mathematics, there seem to be a lot of different types of numbers. What exactly are: Real numbers Integers Rational numbers Decimals Complex numbers Natural numbers Cardinals …

In $\sqrt {45} \approx 6.708$ the left side is not rational but the right side is. Approximate equality does not preserve rationality; indeed to know whether a number is rational it is of no use …

Sep 5, 2011 · I am trying to figure out how to prove that all rational numbers are either terminating decimal or repeating decimal numerals, but I am having a great difficulty in doing so. Any help …

May 19, 2015 · If it cannot be written this way, then it is irrational. There is nothing in the definition that prevents a rational number from being written as a fraction in other ways, such as having …

Sep 15, 2015 · However, if you think about algebraic numbers, which are rational numbers and irrational numbers which can be expressed as roots of polynomials with integer coefficients …

Jul 28, 2015 · Well,the 2 statements I mentioned are from wikipedia..so if 0.3333 is both recurring and non terminating then it should be both a rational number (as it is recurring) and irrational …

Between every two real numbers (in particular between two irrational numbers), there are rational numbers (in fact infinitely many of them). Depending on which definition of real numbers you …