# Tagged Questions

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 ...
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? ...
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.
### 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 ...