float x = 3154681.124 / 100000; //x = 31.54;

I want x to be:

x = 31.5468112;
  • 2
    When you write 3154681.124 / 100000, you are accumulating two rounding errors: first, in representing the numerator as a float, then in the division. Total error ≈ 1.09e-6. If you write instead 31.54681124 you have a single rounding error, and the total error is 25% lower. May 10 '16 at 12:01
  • 1
    An IEEE 32 bit float has only 23 bits for the fractional part, so you only get about log(2^23)/log(10)=6.9 decimal places total. Maybe you want a double?
    – Dave X
    May 12 '16 at 16:46

The float type has slightly over 7 digits of precision. See https://en.wikipedia.org/wiki/Floating_point.

I want x to be:

   x = 31.5468112;

Bad luck. That's 9 digits of precision. You can get around 7 digits by converting it appropriately, eg. as Majenko said:

  float x = 3154681.124 / 100000; //x = 31.54;
  Serial.println(x, 7);

However that printed:


It got 7 digits right, as advertised.

You can use the BigNumber Library that I wrote. Available from GitHub.

Using that, you can get all the precision you want, within reason:

#include "BigNumber.h"

void setup ()
  Serial.begin (115200);
  Serial.println ();

  BigNumber::begin (7);  // 7 digits after the decimal place

  BigNumber x ("3154681.124");
  BigNumber y = x / BigNumber ("100000");
  }  // end of setup

void loop ()
  }  // end of loop


float x = 3154681.124 / 100000; //x = 31.54;

x is now 31.5468112 (or close to).


Output: 31.54

Why? Because Serial.println defaults to 2 decimal places for floats.



Serial.println(val, format)


val: the value to print - any data type

format: specifies the number base (for integral data types) or number of decimal places (for floating point types)

So the solution: specift 7 decimal places when you print:

Serial.println(x, 7);
  • I don't want to print x , I want to send it as a parameter in URL to web service. when I send it as x its value became 31.54
    – Amir Hamdy
    May 9 '16 at 21:03
  • Then whatever your code is that is doing the sending is truncating it. I can't see that code, so I can't advise on it. The simple fact, though, is a float doesn't have a fixed number of decimal places, that's not how floats work.
    – Majenko
    May 9 '16 at 21:04
  • when I send it as x its value became 31.54 - you need to post that code. We can't answer questions about code we can't see.
    – Nick Gammon
    May 10 '16 at 5:59

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