EasyTransferI2C library lost data precision in float type. Why?

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So. I try code for extracting integer and fraction part of my data.

//#include <math.h> 
#include <Wire.h>

#include <LiquidCrystal.h>
// initialize the library with the numbers of the interface pins
LiquidCrystal lcd(10, 4, 5, 6, 7, 8);




void setup(){

 lcd.begin(16, 4);
 pinMode(9, OUTPUT);
 Serial.begin(9600) ;
 
}

void loop() 
{
double a = -278.789456; // test value
int val=0;
long frac=0;
double q=0;

val=int(a); //integer part


    if(val >= 0) //fraction part
        frac = (a - int(a)) * 1000000;
    else
        frac = (int(a)- a ) * 1000000;


q=(frac*0.000001)+val;

lcd.setCursor(0,0);
lcd.print(a,6);
lcd.setCursor(0,1);
lcd.print(val);
lcd.setCursor(0,2);
lcd.print(frac);
lcd.setCursor(0,3);
lcd.print(q,6);


}

I have errors:

  1. Lost precision in fraction part.
    data is -278.789456
    On LCD i see -278.789459
    integer part -278 it's ok
    fraction part is 789459 - wrong

  2. Incorrect recovery from integer and fraction part.
    I have -277.210540 on LCD
    I think - my recovery formula - not correct.

Please help with this troubles.

Thanks