# Tagged Questions

19 views

### Shared groceries expenses between roommates to be divided as per specific consumption ratio and attendance

My apologies if this question is in the wrong section. Couple of my roommates & I (total 5 people) share the groceries expenses. We record the purchases in an Excel sheet, and also have the ratio ...
97 views

### How to find the integer part of big number?

How to calculate the integer part $$\left \lfloor10^{10^{10^{10^{10^{-10^{10}}}}}} \right \rfloor ?$$ Does this equal $$10^{10^{10}}?$$ Both Maple and Mathematica fail with it. PS. Unmotivated votes ...
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### IEEE-754 General Issues

I read the documents of the IEEE-754 and I could not understand some things 1) Is it possible to represent any number using this method? I know there are a number of final states, and there are ...
10k views

### Proof that ${\left(\pi^\pi\right)}^{\pi^\pi}$ (and now $\pi^{\left(\pi^{\pi^\pi}\right)}$) is a noninteger

Conor McBride asks for a fast proof that $$x = {\left(\pi^\pi\right)}^{\pi^\pi}$$ is not an integer. It would be sufficient to calculate a very rough approximation, to a precision of less than 1, and ...
93 views

### Aproximate calculation in decimals

I am trying to refresh on precision of calculations. If we have the decimal fractions: $.234673$, $.322135$, $.114342$, $.563217$ each known to be correct to six figures why are each of the decimals ...
251 views

### Significant digits

We use currency conversion rates for financial calculations. Our currency conversion table stores conversion rates to and from each currency (about 150 world currencies) for each day, going back 20 ...
125 views

### Different Representations of Numbers in Subsets of $\mathbb R$

I think I've mentioned sometime before about logarithmic number system. In this system, a real number $r$ is represented by $(\text{sgn}(r), \log|r|) \in \{-1, 0, 1\} \times \mathbb R$. If $\mathbb R$ ...
527 views

### How many decimal places are needed for incremental average calculation?

If using the following formula to incrementally calculate average value: $$m_n = m_{n-1} + \frac{a_{n}-m_{n-1}}{n}$$ And the number of decimal places to where you can save $m_n$ is limited to $d$ ...
208 views

### How can I write an algorithm to perform the following calculation exactly? (references accepted)

Given natural numbers $N, K, m, C$, with $3^{m/3}K>C$, I want to be able to write an algorithm to exactly compute the number $$\left\lceil \log_3 \left(\frac{N}{3^{m/3}K-C}\right) \right\rceil$$ ...
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### 1/3+2/3 in double precision

When I add 1/3 and 2/3 in double precision, I ended up with $1.\boxed{111\ldots1}1\times2^{-1}$, where the boxed part is the 52-bit mantissa. By the rounding to even rule, I should round it up, right? ...
2k views

### How can I calculate non-integer exponents?

I can calculate the result of $x^y$ provided that $y \in\mathbb{N}, x \neq 0$ using a simple recursive function:  f(x,y) = \begin {cases} 1 & y = 0 \\ (x)f(x, y-1) & y > 0 \end ...
### Need faster division technique for $4$ digit numbers.
I have to divide $2860$ by $3186$. The question gives only $2$ minutes and that division is only half part of question. Now I can't possibly make that division in or less than $2$ minutes by applying ...