Why does static_cast return wrong value?

Question

C++ / C#

Good day. I study C++ according to R. Laforet's book "OOP in C++".
There was a problem in the program

#include <iostream>
#include <clocale>
using namespace std;
int main()
{
  setlocale(LC_CTYPE, "rus");
  float a, c, k;
  int b, z;
  cout << "Введите количество фунтов: " << endl;
  cin >> a;
  b = static_cast<int>(a);
  c = a - b;
  c *= 20;
  z = static_cast<int>(c);
  k = c - z;
  k *= 12;
  k = static_cast<int>(k);
  cout << "Эквивалентная сумма в старой форме записи: J" <<b<<"."<<z<<"."<<k<< endl;
  return 0;
}

If the user enters for example 8.65, then after the lines

c *= 20;
z = static_cast<int>(c);

it turns out that z=12. Although it should actually be 13.
Let c=0.65*20, then z = static_cast(13). And accordingly, when selecting the integer part from 13, we should get 13. Help me understand the problem.

Answer 1

0.65 cannot be represented in memory as exactly 0.65
Use double instead of float

Answer 2

0.65 = 65 / 100 = 13 / (2 * 2 * 5). This fraction cannot be represented in the final form as a binary number, since its denominator contains numbers other than 2. Therefore, calculations with its participation are approximate.

Answer 3

So use the functions specially designed for this from math.h (cmath). And even double will not help you in all situations.