# Questions tagged [rational-numbers]

Questions about numbers expressible as the quotient of two integers. For questions on determining whether a number is rational, use the (rationality-testing) tag instead.

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### relation between rational and irrational, non-transcendental numbers?

a long time ago, when watching a video about continued fractions, I saw something interesting, all continued fractions in that video (all that were non-transcendental) had a rational-looking fraction. ...
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### What are the Laws of Rational Exponents?

On Math SE, I've seen several questions which relate to the following. By abusing the laws of exponents for rational exponents, one can come up with any number of apparent paradoxes, in which a number ...
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### Significant figures problems

Between my first assessments I met some exercices that I don't know how to do them because I did not understand well the rules or maybe I applied in a wrong manner. For instance: The following ...
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### Proving an inequality between the difference of $\sqrt2$ and any rational number. [duplicate]

Let $a = \sqrt{2}$ Prove that for every $m,n\in N$ $|a - \frac{m}{n}| \gt \frac{1}{(2\sqrt2+1)n^2}$ Hint: Consider $|a - \frac{m}{n}|\geq 1$ and $|a - \frac{m}{n}|\leq 1$ as separate cases and ...
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