4
votes
2answers
4k views

Is a non-repeating and non-terminating decimal always an irrational?

We can build $\frac{1}{33}$ like this, $.030303$ $\cdots$ ($03$ repeats). $.0303$ $\cdots$ tends to $\frac{1}{33}$. So,I was wondering this: In the decimal representation, if we start writing the ...
23
votes
5answers
3k views

How do you calculate the decimal expansion of an irrational number?

Just curious, how do you calculate an irrational number? Take $\pi$ for example. Computers have calculated $\pi$ to the millionth digit and beyond. What formula/method do they use to figure this out? ...
2
votes
4answers
488 views

Computing decimal digits of irrational numbers

How to compute the decimal digits of irrational number(non-transcendental) with an arbitrary precision? eg. Expansion of $\sqrt{ 2}$ with a precision of 500.
0
votes
3answers
186 views

What is $\{y\in\mathbb Q\mid y=\cos(x),\quad x\in[0,2\pi]\cap\mathbb Q\}?$

Given a range of the rational numbers, $x$, between $0$ and $2\pi$\, what is the set of rational numbers $ y = \cos(x) $? I was inspired by the stackoverflow question Can $\cos(a)$ ever equal $0$ in ...