Multiplication with floats is wrong for some reason - c++

Question

SOk I edited out all the irrelevant information. Also I did some testing on a new file and it seems when you multiply two numbers that are being put in variables against each other it produces the wrong result. Like in my code the user is entering the length in feet first then in inches. The inches is then divided by 12 and added with feet. Also there getting rounded. Same goes for the width. Then when you multiply the length and width together it produces the wrong result.
Why is that? How do I fix it?
using namespace std;
void setdata();
int main(){
setdata();
return 0;
}
void setdata(){
int idnumber, lengthfeet, lengthinches, widthfeet, widthinches;
float costsqfoot, discount, lengthinchdec, widthinchdec, foot1, reallength, realwidth, arearoom;
foot1= 12;
cout << "What is length of room \t Feet: "; cin >> lengthfeet; cout << "\t \t \t Inches: "; cin >> lengthinches;
cout << "What is width of room \t Feet: "; cin >> widthfeet; cout << "\t \t \t Inches: "; cin >> widthinches;
cout << fixed << setprecision(2);
lengthinchdec = lengthinches / foot1; cout << lengthinchdec << endl; widthinchdec = widthinches / foot1; cout << widthinchdec;
reallength = lengthfeet + lengthinchdec; realwidth = widthfeet + widthinchdec; arearoom = (reallength * realwidth);
cout << endl;
cout << reallength << endl; cout << realwidth << endl;
cout << arearoom;
}
example
input for length feet:30
input for length inch: 5
input for width feet: 18
input for width inch: 11
Output for reallength is 30.42. The lengthinches is being divided by 12 so 5/12 is .42 when rounded up.
Output for realwidth is 18.92. The widthinches is being divided by 12 so 11/12 is .92 when rounded up.
The answer comes out 575.38.
It's supposed to come out 575.54

Answer 1

For your checking on the calculator, you're rounding up the intermediate results.
Your program isn't rounding the intermediate results, only the result of the multiplication.
575.38 is the correct answer!

Answer 2

Imperial units hell :)
multiplied it by hand and got
30 feet 5 inches * 18 feet 11 inches = 82 855 inches2
which is 575.38194444444 sqf
so... what is the problem?
and just for fun formatted the code and pushed it into CoLiRu with all variables set to double instead of float, just in case... http://coliru.stacked-crooked.com/a/2fcef984c5561159 and got the same result

Answer 3

Floating point calculations may be tricky. Values like the result of 5/12 aren't representable by a binary floating point number with a finite number of digits, so they are calculated and stored in float or a double types with a certain amount of rounding errors.
In some cases (like your particular example), one can avoid those errors (even if negligible in practice) using integer arithmetic instead.
Consider this snippet of code and how it deals with your problem:
#include <iostream>
#include <iomanip>
int main() {
using std::cout;
using std::cin;
constexpr int inches_in_one_foot = 12;
constexpr int square_inches_in_one_square_foot =
inches_in_one_foot * inches_in_one_foot;
// Please, note that in real code user input should be checked
int length_feet, length_inches, width_feet, width_inches;
cout << "What is the length of the room?\nFeet: ";
cin >> length_feet;
cout << "Inches: ";
cin >> length_inches;
cout << "What is the width of the room?\nFeet: ";
cin >> width_feet;
cout << "Inches: ";
cin >> width_inches;
// calculate the dimensions in inches
int length = length_inches + inches_in_one_foot * length_feet;
int width = width_inches + inches_in_one_foot * width_feet;
// the area is precisely calculated in square inches
int area = length * width;
int area_feet = area / square_inches_in_one_square_foot;
// note that this ^^^ is an integer division, or: 82855 / 144 = 575
int area_inches = area - area_feet * square_inches_in_one_square_foot;
cout << "\nArea: " << area_feet << " square feet and "
<< area_inches << " square inches.\n";
cout << "or : " << std::fixed << std::setprecision(2)
<< static_cast<float>(area) / square_inches_in_one_square_foot
<< " square feet.\n";
return 0;
}
Entering the values 30 5 18 11, it gaves the following output:
Area: 575 square feet and 55 square inches.
or : 575.38 square feet.
Note that in the second result, the decimal part doesn't represent 38 square inches, but 0.38 square feet, as a two figures approximation of the value 0.381944.