# Tagged Questions

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

2answers
2k views

### When I can assume that all decimal digits returned by Mathematica are provably correct?

How to Control the Precision and Accuracy of Numerical Results Arbitrary-Precision Numbers Mathematica works with exact numbers and with two different types of approximate numbers: machine-...
3answers
775 views

### Real Numbers in the Wolfram Language

Epilog: Much of the discussion in the answers below revolves around the distinction between Real as a data type and real numbers as a domain or class of numbers (irrespective of the form in which ...
6answers
2k views

### Formatting a fraction as a mixed number

Is there a command that will take a rational number and rewrite it in a mixed-number-like form? That is, I'd like to apply a command to something like 10/7 and get ...
5answers
968 views

### Is this the most efficient way to round approximate integers to integers while leaving other Reals untouched?

This might seem like an overly simple question, but I need to specify custom plot tick marks as integers (no trailing decimal point) if they are approximately integers, but not if they are not. Using <...
4answers
3k views

### How to implement Donald Knuth's up-arrow notation

How does one enter very large numbers in up-arrow notation? Up-arrow notation was created by Donald Knuth to write very large numbers in it iterated exponentiation form, for example 6↑↑3 = 6^6^6.
1answer
10k views

### Entering numbers in Scientific Notation?

I need to play with a lot of powers such as 10^-3. 1E-3 does not work for it. Is there any short form for it?
5answers
246 views

### Tidy form of numbers with errors using ScientificForm

Say I've computed something and got a number 0.02112398 with a computed error: 0.000331 Formatting it with ScientificForm[0.02112398 \[PlusMinus] 0.000331] gives me:...
1answer
833 views

### Number format in Legend Labels

I would like to use the usual (new and nice) BarLegend[] with something like BarLegend[{"LakeColors", 1/10000 {-2, 2}}] which ...
2answers
3k views

### Convert a string to hex number?

How can I convert a string containing a hex number such as "6b" to a hex digit that mathematica can use to do math with? I have tried using ...
3answers
973 views

### Expression of uncertainty in measurement.

I have a problem with writing a Mathematica function. I have been requested to show the results of my experiments with the measurement uncertainty (mu) like below: ...
1answer
258 views

### 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 (...
4answers
2k views

### How to plot logarithmic scales

How can a simple logarithmic number line be drawn between any 2 integer values? The closest function I found in the documentation is LogLinearPlot[] and I've ...
1answer
2k views

### How do I get Mathematica to show a number in non-exponential form? [duplicate]

Sometimes I make a calculation in Mathematica that produces a big number, which Mathematica shows like so: -1.52522*10^7 This is annoying to me, because I want ...
2answers
294 views

### 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: ...
6answers
199 views

### Join decimal part

I have a list of mesures that each vector is like {0,1,-2,259} but it should be like {0.1,-2.259} So I did a rule, like ...
2answers
2k views

### Converting numbers to integers

I've read the available documentation but I still haven't found an NumberForm -> Integer function yet. No result in this site's search, either. Does it exist? ...
1answer
262 views

### Machine Epsilon

I'm trying to evaluate the machine epsilon of my computer (see below). I wrote this: ...
2answers
536 views

### Fast Karatsuba Squaring, how to?

I want to improve timing of squaring for big numbers. So I asked What is the fastest way to split a number into parts and What is the most efficient way to add zeros to end of a number with several ...
3answers
202 views

### How can I improve NumberString?

I would like to test strings to see if they represent numbers. This should include number representations with precision marks and scientific notation. NumberString ...
2answers
159 views

### 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 ...
2answers
151 views

### Showing AlgebraicNumber[1/2 (1 + Sqrt[5]), {-3, 2}] in human-readable way

Is there a function to show algebraic numbers in Mathematica more conveniently? I am looking for something similar to MatrixForm for matrices. For example, I would like to view ...
2answers
147 views

### Display All Output Numbers in HEX

How might I modify Mathematica such that I can get the following functionality when working with HEX values. The odd lines are input and the even output. Red values should be the HEX values. ...
0answers
184 views

### 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 ...
3answers
303 views

### What is the FullForm of 36^^sadjh.87s567*^-34?

The Mathematica parser parses and computes number literals before sending them to FullForm even if Hold is applied. Thus the ...
2answers
378 views

### What is the most efficient way to add zeros to end of a number?

Beside *10^n, is there a faster way to add thousands of zeros to end of a number? Updated Timings: ...
4answers
2k views

### Convert Integer to Real [duplicate]

Is there a preferred way of converting an Integer to a Real? What I'm using at the moment is ...
1answer
84 views

### 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 ...
0answers
71 views

### 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 ...
2answers
758 views

### decompose a number (less than 255) in a sum of powers of 2

Is there a built in function that would take a number and decompose it into a sum of powers of 2? The numbers will be non negative less than 256. For what it's worth I'm trying to understand a paper ...
3answers
374 views

### Customizing decimal mark used in plot frame tick labels

I am using the Plot function in a usual way. I use Mathematica 9.0.1.0 in English (I do not know if it is available in other languages, but I do not mind), and as a ...
2answers
698 views

### hexList[[1]] returns a list of decimal numbers

Sorry for not being clear about this question earlier. I appreciate the answers I got, but the edits I made should make the question more understandable. I have been working with hex in Mathematica,...
1answer
109 views

### Is there a Real equivalent to FromDigits?

One can extract an Integer's digits using IntegerDigits and reassemble them into the Integer ...
2answers
574 views

### 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?
2answers
546 views

### Representation of negative exponents [duplicate]

Possible Duplicate: Way to improve “show me this decimal number to M places, don't use scientific notation”? How can I expand e.g. number 1.*10^-8 so that there would be no ...
3answers
106 views

### Testing for a vector of reals [closed]

Suppose I define: RealVector[expr_]:=VectorQ[expr,NumberQ[#]&&Head[#]===Real)]; Then: ...
1answer
88 views

### Calculations after NumberForm [duplicate]

As specified in documentation center the functions AccountingForm, NumberForm, etc. are useful only to display numbers in ...
1answer
81 views

### Range and decimal digits [duplicate]

When I set Plot[Sin[x], {x, -2, -1}, Frame -> True, Axes -> False, FrameTicks -> {{Automatic, Automatic}, {Range[-2, -1, 0.2], Automatic}}] I ...
1answer
58 views

Considering we have a string: str = "1a 789 4/7 123/7 asff %$#7 478 9/4" How can I insert "/1" for the numbers that are ... 1answer 87 views ### Converting a quantity to a decimal form [closed] I have a function giving me this: (5 Coulomb)/(6 Second) as output. I want this in decimal form and would like to have the variables taken off the end for unit ... 1answer 34 views ### 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: ... 2answers 101 views ### How to interpret and show an input number with the amount of significant digits given? what can I do to have Mathematica intepret and show a number with exactly the amount of digits I gave as an input? I have a larger talbe with numbers (text file, whitespace seperated) which are ... 0answers 56 views ### Rationalize error The docs state that "Rationalize[x,dx] yields the rational number with smallest denominator that lies within dx of x." However, testing this out it appears to be false. ... 3answers 162 views ### 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. ... 1answer 190 views ### Something wrong with FromDigits? NestList[RotateLeft, IntegerDigits[19], 1] FromDigits[%] (* WRONG *) ... 2answers 95 views ### Arithmetic on algebraic numbers I'd like to perform some elementary operations on algebraic numbers. ... 2answers 118 views ### 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 ...
3answers
125 views

### 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 ...
2answers
45 views

### 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 ...
1answer
60 views

### 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 ...
1answer
53 views

### 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, ...