How to display very small numbers in Mathematica?












2












$begingroup$


I am trying to evaluate the function:
$$f(x) = cos(x) - mathrm{e}^{-2.7 x}$$
at $x = 1.7 times 10^{-25}$



and Mathematica keeps returning '0.'



How do I evaluate the expression in a better way?






precision-and-accuracy







share|improve this question









New contributor




Ray_56 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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    2












    $begingroup$


    I am trying to evaluate the function:
    $$f(x) = cos(x) - mathrm{e}^{-2.7 x}$$
    at $x = 1.7 times 10^{-25}$



    and Mathematica keeps returning '0.'



    How do I evaluate the expression in a better way?






    precision-and-accuracy







    share|improve this question









    New contributor




    Ray_56 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
    Check out our Code of Conduct.







    $endgroup$















      2












      2








      2





      $begingroup$


      I am trying to evaluate the function:
      $$f(x) = cos(x) - mathrm{e}^{-2.7 x}$$
      at $x = 1.7 times 10^{-25}$



      and Mathematica keeps returning '0.'



      How do I evaluate the expression in a better way?






      precision-and-accuracy







      share|improve this question









      New contributor




      Ray_56 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.







      $endgroup$




      I am trying to evaluate the function:
      $$f(x) = cos(x) - mathrm{e}^{-2.7 x}$$
      at $x = 1.7 times 10^{-25}$



      and Mathematica keeps returning '0.'



      How do I evaluate the expression in a better way?






      precision-and-accuracy




      precision-and-accuracy






      share|improve this question









      New contributor




      Ray_56 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.











      share|improve this question









      New contributor




      Ray_56 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.









      share|improve this question




      share|improve this question








      edited 18 mins ago









      Henrik Schumacher

      50.8k469145




      50.8k469145






      New contributor




      Ray_56 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.









      asked 3 hours ago









      Ray_56Ray_56

      111




      111




      New contributor




      Ray_56 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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      New contributor





      Ray_56 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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      Check out our Code of Conduct.






















          4 Answers
          4






          active

          oldest

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          1












          $begingroup$

          Can also use exact numbers.



          f[x_] = Cos[x] - E^(-27 x/10);
          

          
f[17 10^-26]//N[#,50]& 
          
   (*4.5899999999999999999999988020950000000000000000002*10^-25*)





          share|improve this answer









          $endgroup$





















            1












            $begingroup$

            The simplest methods are usually the best. Try this code



            N[Cos[x] - Exp[-x 27/10] /. x -> 17*^-26, 15] // InputForm


            or a minor variation



            With[{x = 17*^-26}, N[Cos[x] - Exp[-x 27/10], 15]] // InputForm


            or define a function first



            f = Cos[#] - Exp[-# 27/10] &; N[f[17*^-26], 15] // InputForm


            All of these return the result



            4.589999999999999999999998802094999`15.*^-25


            You can get more digits by increasing the 15 digits precision.



            For example, with 34 digits precision the result returned is



            4.5899999999999999999999988020950000000000000000001613`34.*^-25





            share|improve this answer











            $endgroup$





















              1












              $begingroup$

              First convert the expression to trigonometric form:



              y = Cos[x] - Exp[-2.7*x] // ExpToTrig



              Cos[x] - Cosh[2.7 x] + Sinh[2.7 x]




              y /. x -> 1.7*10^-25



              4.59*10^-25




              This is the exact solution.






              share|improve this answer











              $endgroup$





















                0












                $begingroup$

                Do a series expansion:



                Series[Cos[x] - Exp[-2.7 x], {x, 0, 1}]


                (*



                SeriesData[x, 0, {2.7}, 1, 2, 1]



                *)



                Then plug in $x = 1.7 times 10^{-25}$ to get:



                $$4.59 times 10^{-25}$$






                share|improve this answer









                $endgroup$













                  Your Answer





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                  4 Answers
                  4






                  active

                  oldest

                  votes








                  4 Answers
                  4






                  active

                  oldest

                  votes









                  active

                  oldest

                  votes






                  active

                  oldest

                  votes









                  1












                  $begingroup$

                  Can also use exact numbers.



                  f[x_] = Cos[x] - E^(-27 x/10);
                  

                  
f[17 10^-26]//N[#,50]& 
                  
   (*4.5899999999999999999999988020950000000000000000002*10^-25*)





                  share|improve this answer









                  $endgroup$


















                    1












                    $begingroup$

                    Can also use exact numbers.



                    f[x_] = Cos[x] - E^(-27 x/10);
                    

                    
f[17 10^-26]//N[#,50]& 
                    
   (*4.5899999999999999999999988020950000000000000000002*10^-25*)





                    share|improve this answer









                    $endgroup$
















                      1












                      1








                      1





                      $begingroup$

                      Can also use exact numbers.



                      f[x_] = Cos[x] - E^(-27 x/10);
                      

                      
f[17 10^-26]//N[#,50]& 
                      
   (*4.5899999999999999999999988020950000000000000000002*10^-25*)





                      share|improve this answer









                      $endgroup$



                      Can also use exact numbers.



                      f[x_] = Cos[x] - E^(-27 x/10);
                      

                      
f[17 10^-26]//N[#,50]& 
                      
   (*4.5899999999999999999999988020950000000000000000002*10^-25*)






                      share|improve this answer












                      share|improve this answer



                      share|improve this answer










                      answered 1 hour ago









                      Bill WattsBill Watts

                      3,0811518




                      3,0811518























                          1












                          $begingroup$

                          The simplest methods are usually the best. Try this code



                          N[Cos[x] - Exp[-x 27/10] /. x -> 17*^-26, 15] // InputForm


                          or a minor variation



                          With[{x = 17*^-26}, N[Cos[x] - Exp[-x 27/10], 15]] // InputForm


                          or define a function first



                          f = Cos[#] - Exp[-# 27/10] &; N[f[17*^-26], 15] // InputForm


                          All of these return the result



                          4.589999999999999999999998802094999`15.*^-25


                          You can get more digits by increasing the 15 digits precision.



                          For example, with 34 digits precision the result returned is



                          4.5899999999999999999999988020950000000000000000001613`34.*^-25





                          share|improve this answer











                          $endgroup$


















                            1












                            $begingroup$

                            The simplest methods are usually the best. Try this code



                            N[Cos[x] - Exp[-x 27/10] /. x -> 17*^-26, 15] // InputForm


                            or a minor variation



                            With[{x = 17*^-26}, N[Cos[x] - Exp[-x 27/10], 15]] // InputForm


                            or define a function first



                            f = Cos[#] - Exp[-# 27/10] &; N[f[17*^-26], 15] // InputForm


                            All of these return the result



                            4.589999999999999999999998802094999`15.*^-25


                            You can get more digits by increasing the 15 digits precision.



                            For example, with 34 digits precision the result returned is



                            4.5899999999999999999999988020950000000000000000001613`34.*^-25





                            share|improve this answer











                            $endgroup$
















                              1












                              1








                              1





                              $begingroup$

                              The simplest methods are usually the best. Try this code



                              N[Cos[x] - Exp[-x 27/10] /. x -> 17*^-26, 15] // InputForm


                              or a minor variation



                              With[{x = 17*^-26}, N[Cos[x] - Exp[-x 27/10], 15]] // InputForm


                              or define a function first



                              f = Cos[#] - Exp[-# 27/10] &; N[f[17*^-26], 15] // InputForm


                              All of these return the result



                              4.589999999999999999999998802094999`15.*^-25


                              You can get more digits by increasing the 15 digits precision.



                              For example, with 34 digits precision the result returned is



                              4.5899999999999999999999988020950000000000000000001613`34.*^-25





                              share|improve this answer











                              $endgroup$



                              The simplest methods are usually the best. Try this code



                              N[Cos[x] - Exp[-x 27/10] /. x -> 17*^-26, 15] // InputForm


                              or a minor variation



                              With[{x = 17*^-26}, N[Cos[x] - Exp[-x 27/10], 15]] // InputForm


                              or define a function first



                              f = Cos[#] - Exp[-# 27/10] &; N[f[17*^-26], 15] // InputForm


                              All of these return the result



                              4.589999999999999999999998802094999`15.*^-25


                              You can get more digits by increasing the 15 digits precision.



                              For example, with 34 digits precision the result returned is



                              4.5899999999999999999999988020950000000000000000001613`34.*^-25






                              share|improve this answer














                              share|improve this answer



                              share|improve this answer








                              edited 35 mins ago

























                              answered 50 mins ago









                              SomosSomos

                              4778




                              4778























                                  1












                                  $begingroup$

                                  First convert the expression to trigonometric form:



                                  y = Cos[x] - Exp[-2.7*x] // ExpToTrig



                                  Cos[x] - Cosh[2.7 x] + Sinh[2.7 x]




                                  y /. x -> 1.7*10^-25



                                  4.59*10^-25




                                  This is the exact solution.






                                  share|improve this answer











                                  $endgroup$


















                                    1












                                    $begingroup$

                                    First convert the expression to trigonometric form:



                                    y = Cos[x] - Exp[-2.7*x] // ExpToTrig



                                    Cos[x] - Cosh[2.7 x] + Sinh[2.7 x]




                                    y /. x -> 1.7*10^-25



                                    4.59*10^-25




                                    This is the exact solution.






                                    share|improve this answer











                                    $endgroup$
















                                      1












                                      1








                                      1





                                      $begingroup$

                                      First convert the expression to trigonometric form:



                                      y = Cos[x] - Exp[-2.7*x] // ExpToTrig



                                      Cos[x] - Cosh[2.7 x] + Sinh[2.7 x]




                                      y /. x -> 1.7*10^-25



                                      4.59*10^-25




                                      This is the exact solution.






                                      share|improve this answer











                                      $endgroup$



                                      First convert the expression to trigonometric form:



                                      y = Cos[x] - Exp[-2.7*x] // ExpToTrig



                                      Cos[x] - Cosh[2.7 x] + Sinh[2.7 x]




                                      y /. x -> 1.7*10^-25



                                      4.59*10^-25




                                      This is the exact solution.







                                      share|improve this answer














                                      share|improve this answer



                                      share|improve this answer








                                      edited 17 mins ago









                                      Henrik Schumacher

                                      50.8k469145




                                      50.8k469145










                                      answered 1 hour ago









                                      VixillatorVixillator

                                      4497




                                      4497























                                          0












                                          $begingroup$

                                          Do a series expansion:



                                          Series[Cos[x] - Exp[-2.7 x], {x, 0, 1}]


                                          (*



                                          SeriesData[x, 0, {2.7}, 1, 2, 1]



                                          *)



                                          Then plug in $x = 1.7 times 10^{-25}$ to get:



                                          $$4.59 times 10^{-25}$$






                                          share|improve this answer









                                          $endgroup$


















                                            0












                                            $begingroup$

                                            Do a series expansion:



                                            Series[Cos[x] - Exp[-2.7 x], {x, 0, 1}]


                                            (*



                                            SeriesData[x, 0, {2.7}, 1, 2, 1]



                                            *)



                                            Then plug in $x = 1.7 times 10^{-25}$ to get:



                                            $$4.59 times 10^{-25}$$






                                            share|improve this answer









                                            $endgroup$
















                                              0












                                              0








                                              0





                                              $begingroup$

                                              Do a series expansion:



                                              Series[Cos[x] - Exp[-2.7 x], {x, 0, 1}]


                                              (*



                                              SeriesData[x, 0, {2.7}, 1, 2, 1]



                                              *)



                                              Then plug in $x = 1.7 times 10^{-25}$ to get:



                                              $$4.59 times 10^{-25}$$






                                              share|improve this answer









                                              $endgroup$



                                              Do a series expansion:



                                              Series[Cos[x] - Exp[-2.7 x], {x, 0, 1}]


                                              (*



                                              SeriesData[x, 0, {2.7}, 1, 2, 1]



                                              *)



                                              Then plug in $x = 1.7 times 10^{-25}$ to get:



                                              $$4.59 times 10^{-25}$$







                                              share|improve this answer












                                              share|improve this answer



                                              share|improve this answer










                                              answered 2 hours ago









                                              David G. StorkDavid G. Stork

                                              23.9k22153




                                              23.9k22153






















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