# Tagged Questions

Questions about interpretation of numeric input or how Mathematica stores and manipulates numbers internally.

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### Copy-pasting a floating point number [duplicate]

Here is a behavior of the Mathematica front end which confuses me. Type N[Sqrt[2]] The displayed output is 1.41421 ...
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### How can I completely discard decimals after a set number of significant figures?

I have a number with a long decimal tail, like x=1.23456789789456123 and I would like to (i) keep the first $n$ significant figures, and (ii) completely discard ...
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### How to round all the numbers in a function?

I have a complicated function that is a combination of floating-point numbers and variables. I want all the numbers rounded off, but I have no clue how to do this. For example I would want ...
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### 4-digit number, where $d_{1000} \lt d_{100} \lt d_{10}\lt d_{1}$ [closed]

I need to find all 4-digit numbers, where ones-number > tens-number > hundreds-number > thousands-number. 6789 is the highest possible such number and 1234 is the lowest. One solution is to write them ...
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### RealDigits and functional style

So while thinking about Replacing numbers of which you only know certain digits I have faced, again, a problem that I find hard to extract from RealDigits' output ...
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### NumberForm pesky warning from Manipulate

I'm using the NumberForm command inside a Manipulate environment, and in some special cases Mathematica gives a pesky and mostly useless warning message : NumberForm::sigz: In addition to the ...
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### How to refer a number in a list with two columns, first one is a number and the second one is empty? [closed]

Let's say, I have defined a list as list = {{-31, -31}, {52, }, {34, -11}, {-38, }, {78, -44}, {-36,14}, {-9, 98}, {33, 6}, {82, 99}, {-85, -10}} As you can see, ...
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### How to get the $0$ result for this limit?

Consider the following series: $$\sigma (\text{x\_})\text{:=}\sqrt{\sum _{k=0}^{x-1} \frac{(x! x!) (-1)^{x-k}}{(x-k) (k! (2 x-k)!)}+\frac{\pi ^2}{12}}$$ From the following codes, it seems that the ...
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### Encoding/Decoding matrices as integers, integers as matrices [closed]

I want to convert large binary matrices of m x n dimensions into integers, and then to convert these integers to the original matrices. I attempted the following: ...
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### Pattern that matches numbers in the $\epsilon$-neighborhood of a given number?

I dfined the following function to create a pattern that matches the $\epsilon$-neighborhood of a given number. ep[x_, e_] := _?(x - e <= # <= x + e &) ...
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### Maintaining working precision in my program

I am badly stuck with this program I am writing. I want output of program below to be precise up to 25 digits after decimal point. I am supplying all inputs with precision 25. But after each iteration ...
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### How to make pairs of Young diagrams appear?

I have the following Young diagrams {{{0}, {2}}, {{0}, {1, 1}}, {{1}, {1}}, {{2}, {0}}, {{1, 1}, {0}}} where you can interpret each pair as following: For ...
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### Mod[1.2, 0.2] is not equal to zero

Why doesn't the following expression evaluate to zero? In[1]:=Mod[1.2, 0.2] Out[1]=0.2 Edit: This is what I wanted to do: ...
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### Behaviour of RealDigits expected or wrong?

Is this behavior expected or a bug? RealDigits[10304.390456] {{1, 0, 3, 0, 4, 3, 9, 0, 4, 5, 5, 9, 9, 9, 9, 9}, 5} when I ...
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### Making a replacement on the numerator and denominator of a rational number

It's isn't a big deal, but when I run the following I don't get the output I expect. After discussing this in the comments it appears it has to do with being an atomic expression. ...
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### Calculations after NumberForm [duplicate]

As specified in documentation center the functions AccountingForm, NumberForm, etc. are useful only to display numbers in ...
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### Is there a global setting for number form

I'm creating strings which represent equations in C to use with library link. The problem I have is that numbers in ScientificForm are no longer useful after they ...
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### NumberLinePlot: How to make the 3rd list (c) appears with “black crosses” or “void circles”?

a = {1, 2, 5, 2} b = {2} c = {1.75, 2.88, 3.25} NumberLinePlot[{a, b, c}, PlotStyle -> Directive[PointSize[0.032]]] I thought about PlotMarkers or PlotStyle, ...
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### Enter exact rational numbers easily with decimal notation

Is there a simple way to enter decimal numbers such as 0.123 so that Mathematica interprets it as an exact rational number 123/1000?
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### The precision of the number

I have problem in Mathematica with unnecessary rounding which is caused by high precision. For example I have value a = 2.052685846*10^-1865, when I make ...
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### Square root of a value defined in a finite field?

I am trying to find the right way to compute the square root of a number defined in a finite field. For example, ...
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### NMinimize seems to call function with the same values multiple times

I have to minimize a function where the evaluation of one parameter set takes very long (around 5sec) and discovered alongside, that NMinimize seems to call this ...
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### Is it possible to lower the bitwidth of (floating point) numbers?

The answer to this question will most probably be a definite no. Nevertheless, I would like to know whether it is possible to represent reals in the memory on less than the standard 32 or 64 bits (...