# Get the precise value of 2^0.3

Posted 10 years ago
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 I am using Mathematica 8.0.1.I learned Mathematica by myself, and till yesterday I didn't need any feature of Mathematica that is related with precision. But today I have to calculate some complicated formula... and the result should bequite precise.I knew that N[Pi, 40] gives the value of Pi upto 40 digits.So we get 3.141592653589793238462643383279502884197I wanted to get the value of 2^0.3, upto 40 digits. So I typedN[2^0.3, 40]But the result was not satisfactory. It just gave me 1.23114Only 6 digits below the point.I empirically know that if I copy a numerical value and paste it on a blank space in Mathematicaone can get better result.... I copied 1.23114 and paste in on a blank space then I get1.2311444133449163But it too is far from 40 correct digits..How can I get the precise value upto 40 digits ?And what is the reason that N[2^0.3, 40] does not give 40 digits ?Thank you very much!
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Posted 10 years ago
 Found the Preferences thing:
Posted 10 years ago
 I have not been able to find the setting in Preferences which sets the number of digits to be shown when computing with approximate real numbers.But it can be done through Option Inspector:
Posted 10 years ago
 For your question,     I want to know that if there is a command such that if I type the command in Mathematica, then from the moment, every calculation is correct up to 30 digits.There isn't.  It can  be immitated with some programming.   \$Pre could take a function that makes all numbers 30-digit Reals.
Posted 10 years ago
 the 0.3 in your expression is assumed to have machine precision unless you indicate anything else, e.g. as 0.340. Recommendation: make it exact, then have N display as many digits as you want: In[1]:= N[2^(3/10), 500]  Out[1]= 1.\ 2311444133449162844993930691677431098761377611008177943370655382461007\ 1971935845840402274965089414163879015210459029977791740537864662955570\ 2613997691724733231558814007022109972283688802144111013437208936735367\ 5027231625935739266842338009115208074805416548016365456080998956820503\ 7313855248205883337415538175614392814574320010634650787696020195377044\ 7150320962601865505947644110111023427053849800553471650411634631084313\9001571098113390373882353914706287757320079410633747638134547549531222\793642897
Posted 10 years ago
 I am using Mathematica 8.0.1.I learned Mathematica by myself, and till yesterday I didn't need any feature of Mathematica that is related with precision. But today I have to calculate some complicated formula... and the result should bequite precise.I knew that N[Pi, 40] gives the value of Pi upto 40 digits.So we get 3.141592653589793238462643383279502884197I wanted to get the value of 2^0.3, upto 40 digits. So I typedN[2^0.3, 40]But the result was not satisfactory. It just gave me 1.23114Only 6 digits below the point.I empirically know that if I copy a numerical value and paste it on a blank space in Mathematicaone can get better result.... I copied 1.23114 and paste in on a blank space then I get1.2311444133449163`But it too is far from 40 correct digits..How can I get the precise value upto 40 digits ?And what is the reason that N[2^0.3, 40] does not give 40 digits ?Thank you very much!
Posted 10 years ago
 Maybe you wish to use SetPrecision[2^0.3, 40]. Detailed information can be found in the tutorial for Arbitrary Precision Numbers and references to Precision & Accuracy Control.
Posted 10 years ago
 N[2^0.3,40] first finds 2^0.3 accurate to about 6 digitsA very minor remark, actually 2^0.3 is computed with full machine precision, see for example InputForm[2^0.3]. There is a setting in Preferences, which controls how many digits are displayed, and that defaults to 6.
Posted 10 years ago
 Calculate the result exactly without using any decimal points and then ask for 40 digit approximation.In[1]:= N[2^(3/10), 40]Out[1]= 1.231144413344916284499393069167743109876N[2^0.3,40] first finds 2^0.3 accurate to about 6 digits and then gives this result to N[6digitvalue,40] which cannot give you any more than the 6 digit value.
Posted 10 years ago
 Also I want to know that if there is a command such that if I type the command in Mathematica, then from the moment, every calculation is correct up to 30 digits. (Maybe the calculated result will not be correct up to 30 digits, because if there are too many or complex calculations like exponentiations. But I mean I do not mind this. What I only need is in every single calculation Mathematica does not round off up to 30 digits.)