# Numeric calculation with many digits

I try to calculate something like 1.569732312*Pi and by default mathematica returns something like 4.93146 (only 5 digits after floating point), but I believe there is much more digits, especially because Pi has infinite number of digits.

if I do like this

N[1.569732312*Pi, 50]


It still return the same 5 digits 4.93146

As I understand from documentation, I have to use Rationalize[]. If I do like this

N[Rationalize[1.569732312]*Pi, 50]


result is the same 4.93146

and only if I remove 3 digits like this

N[Rationalize[1.569732]*Pi, 50]


it gives me all digits like this

4.9314585193048133197984421233221006214165911156199


What I am doing wrong and how to calculate 1.569732312*Pi with 50 digits precision?

• 1.56973231250*Pi - note the backtick. See also here. – corey979 Oct 31 '16 at 22:18
• Thanks a lot! Yes, if I put something like 1.56973231250*Pi, it works fine. – Zlelik Oct 31 '16 at 22:32
• 1.569732312 is a machine double. What 50 digit result would you expect to get from that product? (If you want a 50 digit number that has 1.569732312 followed by decimal zeroes, the tactic of using 1.56973231250 as proposed by @corey979 is appropriate). – Daniel Lichtblau Oct 31 '16 at 22:33
• I want to know the result of my equation. Like Pi=3.1415926...., If I multiple it by 2, it will be 6,2831852, but I want to know all 50 digits of this equation 2*Pi, because Pi has infinite digits. and later I want to change 2 to some different number. – Zlelik Oct 31 '16 at 22:49
• you should review the details section in the docs for Rationalize to learn whats happening there. – george2079 Nov 1 '16 at 0:55

1.56973231250*Pi