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I've made a Manipulate app. in Mathematica where I vary the value of a function f(a) by varying the parameter a. However, I seem to only be able to edit my input for a for a value up to 5 decimal places (if I enter in a number with more than 5 decimal places, it rounds the figure). Is it possible to increase the number of decimal places with which I can enter in my value of a into the manipulate input?

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I think similar things have been answered here. Search NumberForm and PrintPrecision. –  Mike Honeychurch Oct 13 '12 at 22:25
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Mike is right. mathematica.stackexchange.com/questions/3736/… has the solution: SetOptions[InputNotebook[], PrintPrecision -> 30] –  David Slater Oct 13 '12 at 22:37
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1 Answer

Initially I forgot to specifically address Manipulate. In addition to this post see also:

Manipulating an arbitrary-precision ContourPlot


This question may qualify as a duplicate (I'll let the community votes decide) but it has been asked in a different way so I'll answer it anew.

There are two issues that may be confounded here: input syntax and output formatting.

Input syntax

By default a number entered with a decimal point that has less than 18 digits is interpreted as a machine precision number, while one with more is interpreted as arbitrary precision:

12.                             // Precision
2.7182818284590452              // Precision
2718281828459045.2              // Precision
2.71828182845904523536028747135 // Precision

MachinePrecision

MachinePrecision

MachinePrecision

29.4343

Any number (with or without a decimal point) can be entered with a specific precision by using the ` symbol. A raw ` means MachinePrecision while e.g. `7 means seven digits of precision:

12`      // Precision
12.3`1   // Precision
3.14`20  // Precision

MachinePrecision

1.

20.

Arithmetic between arbitrary and machine precision numbers automatically converts to machine precision:

12.3`1 * 17.2 // Precision

MachinePrecision

See also: Converting to machine precision

Output formatting

Machine precision numbers are by default automatically truncated to six digits in OutputForm, but more digits are still there internally:

2.7182818284590452 // InputForm

2.718281828459045

Methods to control this formatting are presented in: Annoying display truncation of numerical results

One of my own recommendations:

SetOptions[$FrontEndSession, PrintPrecision -> 10]

2.7182818284590452

2.718281828

This Option can be set globally: $FrontEnd, for a session: $FrontEndSession, for a particular Notebook: EvaluationNotebook[], or even for a particular cell or expression (with the Option Inspector for Cells or Style for single expressions).

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