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I was wondering why you wouldn't just use a double all the time instead of a float. I googled and found this as an explanation:
Double is more precise than float and can store 64 bits; double the number of bits float can store. We prefer double over float if we need to do precision up to 15 or 16 decimal points; otherwise, we can stick to float in most applications, as double is more expensive.
Difference between float and double in C/C++ | Coding Ninjas Blog
Can anyone clarify what being "more expensive" means in this context?
To quote the C++ standard, §3.9.1 ¶8:
There are three floating point types: float, double, and long double. The type double provides at least as much precision as float, and the type long double provides at least as much precision as double. The set of values of the type float is a subset of the set of values of the type double; the set of values of the type double is a subset of the set of values of the type long double. The value representation of floating-point types is implementation-defined. Integral and floating types are collectively called arithmetic types. Specializations of the standard template std::numeric_limits (18.3) shall specify the maximum and minimum values of each arithmetic type for an implementation.
That is to say that double takes at least as much memory for its representation as float and long double at least as much as double. That extra memory is used for more precise representation of a number.
On x86 systems, float is typically 4 bytes long and can store numbers as large as about 3×10³⁸ and about as small as 1.4×10⁻⁴⁵. It is an IEEE 754 single-precision number that stores about 7 decimal digits of a fractional number.
Also on x86 systems, double is 8 bytes long and can store numbers in the IEEE 754 double-precision format, which has a much larger range and stores numbers with more precision, about 15 decimal digits. On some other platforms, double may not be 8 bytes long and may indeed be the same as a single-precision float.
The standard only requires that long double is at least as precise as double, so some compilers will simply treat long double as if it is the same as double. But, on most x86 chips, the 10-byte extended precision format 80-bit number is available through the CPU's floating-point unit, which provides even more precision than 64-bit double, with about 21 decimal digits of precision.
Some compilers instead support a 16-byte (128-bit) IEEE 754 quadruple precision number format with yet more precise representations and a larger range.
It depends on your compiler but the following code can show you the number of bytes that each type requires:
int main() {
printf("%d\n", sizeof(double)); // some compilers print 8
printf("%d\n", sizeof(long double)); // some compilers print 16
return 0;
}