How to write in binary file?

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C++

This code should take 3 decimal places from the user and in the binary file
Write then read it, but it does not save anything in the file and does not give errors
What is the problem with writing to a file?

What I have tried:

#include<iostream>
#include<fstream>
using namespace std;

int main()
{
 float num;
 streampos size;
 fstream outputFile;
 char* mem;
 //write from file
  outputFile.open("output.bin", ios::out | ios::app|ios::binary);
  
 for (int i = 0; i < 3; i++)
 {
 
 cout << "Enter float number : ";
 cin >> num;
 cout << endl;
 
 outputFile.write(mem,size );
 
 }
 outputFile.close();
 
 //read from file
  outputFile.open("output.bin", ios::ate | ios::binary);
  if(outputFile.is_open())
  {
      size=outputFile.tellg();
      
      char* mem=new char [size ];
      outputFile.seekg(size,ios::beg);
      outputFile.read(mem,size);
      
        }
outputFile.close();
 return 0;
}