Questions tagged [number-representation]

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

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17
votes
5answers
2k 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 <...
64
votes
3answers
3k views

When can I 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-...
9
votes
3answers
955 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: ...
6
votes
1answer
274 views

Calculations after NumberForm [duplicate]

As specified in documentation center the functions AccountingForm, NumberForm, etc. are useful only to display numbers in ...
11
votes
3answers
1k 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: ...
9
votes
1answer
323 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 (...
2
votes
1answer
105 views

Unexpected behavior from `NumberForm` of a matix [duplicate]

If I calculate the dimension of the matrix after NumberForm directly, then there will be something wrong ...
11
votes
2answers
751 views

Does Mathematica have an equivalent of Python's float.as_integer_ratio?

The Python programming language has a float.as_integer_ratio(x) function which exactly converts an IEEE 754 floating-point number into a numerator/denominator pair ...
7
votes
2answers
891 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?
11
votes
2answers
672 views

Understanding simple numerical calculation

I am trying to understand why N[0.1]//FullForm returns 0.1' (A). Indeed, $0.1$ in base two is $0.000110011001100110011...$. If I ...
6
votes
5answers
1k views

How to get exact Rationalize of a decimal number?

This is on Mathematica 11.1 on Windows 7. I have this value 0.97646105481464028 which I'd like to get exact rational for it. I have thought that every terminating ...
5
votes
3answers
259 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 ...
3
votes
2answers
771 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,...
14
votes
1answer
2k 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 ...
10
votes
2answers
395 views

How to copy formatted numbers as MathML without quotation marks?

I have the following code: a = 6.08717*10^6; b = a/3; c = a*1.5; d = a^2; matrix={{a, b, c, d},{b, c, d, a},{c, d, a, b},{d, a, b, c}}; matrix // EngineeringForm ...
4
votes
1answer
99 views

NumberForm and Precision

With MachinePrecision this construction works as expected ...
6
votes
2answers
3k 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? ...
2
votes
3answers
128 views

Testing for a vector of reals [closed]

Suppose I define: RealVector[expr_]:=VectorQ[expr,NumberQ[#]&&Head[#]===Real)]; Then: ...
0
votes
2answers
200 views

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 ...
23
votes
3answers
1k 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 ...
11
votes
1answer
4k 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 ...
8
votes
1answer
187 views

Arbitrary-Precision Arithmetic behaves unexpectedly

I want to understand how small numerical errors propagate through a computation and may drastically change the final result. To this end, I consider a toy world in which every number is limited to ...
5
votes
3answers
715 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 ...
9
votes
2answers
4k 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 ...
7
votes
1answer
135 views

Problem to import numbers longer than 19-digit with “JSON” or “RawJSON”

Bug introduced in 11.0.1 or earlier and fixed in 12.0. MMA 11.0.1.0 (Windows 10, 64-bit) I see that "JSON" import can be buggy (154245), so my question is simple: can the following behaviour be ...
4
votes
1answer
103 views

ExponentFunction not respected in NumberForm when typesetting zero?

Let's try to typeset a couple of numbers with a precision accuracy of 4: 0``4 1``4 1000000``4 I do not want the numbers returned with ...
3
votes
0answers
135 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. ...
1
vote
0answers
109 views

LieArt — 3 different 8 dimensional irreducible representation of $\mathrm{SO}(8)$ and their decompositions

I am using the LieArt which you can download freely online https://arxiv.org/pdf/1206.6379.pdf There are three different 8 dimensional $\mathrm{SO}(8)$ irreducible representations, formally it is ...
9
votes
1answer
486 views

Machine Epsilon

I'm trying to evaluate the machine epsilon of my computer (see below). I wrote this: ...
5
votes
2answers
228 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. What ...
5
votes
2answers
164 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 ...
5
votes
2answers
123 views

Early vs. late application of arbitrary precision

The following arbitrary-precision computations, in which arbitrary precision is applied early (to the inputs), both work as expected: ...
4
votes
2answers
94 views

StringTemplate does not respect NumberFormat

I am trying to write Latex report generator for my standard data analysis. But there is an issue with formatting numbers I can not get around. I would like to make use of my own ...
4
votes
1answer
160 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 ...
4
votes
2answers
401 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: ...
2
votes
1answer
144 views

How to plot data that are already in scientific form? [duplicate]

I've got an array of data shown in scientific form. Which looks like this: x = {0.0001,ScientificForm[0.999890436521418]} Now I'm trying to use ListPlot to plot ...
2
votes
1answer
263 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 ...
1
vote
1answer
699 views

What is the fastest way to split a number into parts?

I have very large numbers (million digits). number = A*10^partlen + B As of now, I split the numbers by this way: ...
0
votes
1answer
834 views

How can I change the default output number form to accounting form?

By default, large numbers are displayed in scientific form in output like 1.2345 x 10^8 in Mathematica 8.0.4, but I would prefer having numbers in accounting form ...
0
votes
0answers
86 views

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 ...