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Questions tagged [number-representation]

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

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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-...
53
votes
3answers
40k 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?
23
votes
7answers
3k 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 ...
23
votes
3answers
2k 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 ...
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 <...
14
votes
4answers
4k 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.
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 ...
12
votes
5answers
420 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:...
11
votes
2answers
759 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 ...
11
votes
2answers
678 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 ...
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: ...
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 ...
10
votes
2answers
408 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 ...
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 ...
9
votes
4answers
451 views

How to format a number with an error?

I'm having a surprising amount of difficulty in trying to format some numbers with errors. I can't find any previous attempts to do this here or elsewhere and it would surely be of use to the ...
9
votes
3answers
1k 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: ...
9
votes
4answers
2k views

Test if number represents an integer

I can't figure out how to test if a number is an integer. I have found IntegerQ, but this function only checks if the type of the input is an integer, not whether ...
9
votes
1answer
502 views

Machine Epsilon

I'm trying to evaluate the machine epsilon of my computer (see below). I wrote this: ...
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 (...
8
votes
4answers
3k 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 been ...
8
votes
3answers
477 views

How to write an array of repeated numbers as a single number

Let's say we have a random number consisting of an arbitrary number of digits, such as for example 3097. This number can be represented as an array of repeated numbers with Mathematica by typing <...
8
votes
1answer
189 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 ...
7
votes
3answers
446 views

Scientific notation for exact numbers?

Some of my symbolic computations involve many large numbers, e.g.: 37894580188800000000000000000000000000000000000000 As the computation is symbolic, I'd like to leave the numbers in exact form, ...
7
votes
2answers
904 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?
7
votes
1answer
146 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 ...
6
votes
5answers
2k 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 ...
6
votes
6answers
225 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 ...
6
votes
2answers
761 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 ...
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? ...
6
votes
1answer
144 views

Why 2^^1*^k does not work?

Table[2^^1*^k,{k,0,10}] This gives an error, why is that? Also this BaseForm[2 ** 1*^ #, 16] & /@ Range[10] What is ...
6
votes
1answer
282 views

Calculations after NumberForm [duplicate]

As specified in documentation center the functions AccountingForm, NumberForm, etc. are useful only to display numbers in ...
5
votes
3answers
755 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 ...
5
votes
4answers
264 views

How to format natural numbers so that they are 2 digits long?

I want to format all numbers from 1 to 50 so that they are all 2 digits long. desiredOutput={01,02,...,49,50} Digging through the documentation the ...
5
votes
2answers
515 views

Is there a command that does exact numerical conversion of non-exact to exact numbers?

I generally prefer to do all my intermediate calculations with exact numbers, and then round my result at the end. Thus I will typically convert each arbitrary-precision number to its exact equivalent;...
5
votes
3answers
852 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 ...
5
votes
3answers
261 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 ...
5
votes
4answers
8k 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 ...
5
votes
3answers
184 views

Dynamically updated AccountingForm

Bug introduced in 10.4 or earlier and persisting through 11.1.1 CASE:3918306 confirmed I freshly installed Wolfram Mathematica. I can't quite remember how to output a dynamically updated variable ...
5
votes
2answers
166 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
133 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: ...
5
votes
2answers
234 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
0answers
282 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 ...
4
votes
5answers
208 views

Convert decimal value to hexadecimal

How can I convert for example 62343 to a hexadecimal value 45 to a hexadecimal value ? I see I can use: IntegerDigits[62343, 16] = {15, 3, 8, 7} ...
4
votes
5answers
252 views

How to convert list of digits to number? [closed]

I have a list such as: a = {1, 2, 4, 3}; and I want to get the 'number' of the list. For this example, I want to get this number: ...
4
votes
2answers
430 views

Representation of Rational Numbers

Following up on this question I would like to understand the way MMA represents rational numbers. First of all, as Carl Woll suggested, x/y is not a simple ...
4
votes
2answers
330 views

Using FromDigits to convert number strings to numbers

I've loved mathematics for a very long time but am only now beginning my journey to learn to code. The attached image shows the two different outputs (out-5, out 6) for a simple crypto-cypher I'm ...
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: ...
4
votes
2answers
149 views

number format with fixed total digit

How to get an output of number form of a given TOTAL digit? For example, a total digit of 3, then one get 1.00 for 1. ...
4
votes
2answers
95 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
123 views

Self-locating Strings in $\pi$?

According to The Pi-Search Page, in the first 100 million digits of $\pi$ the following numbers are self-locating: 1, 16470, 44899, 79873884. The following inefficient code (which also does not ...