Huge difference.

As the name implies, a double has 2x the precision of float^[1]. In general a double has 15 decimal digits of precision, while float has 7.

Here's how the number of digits are calculated:

double has 52 mantissa bits + 1 hidden bit: log(2⁵³)÷log(10) = 15.95 digits

float has 23 mantissa bits + 1 hidden bit: log(2²⁴)÷log(10) = 7.22 digits

This precision loss could lead to greater truncation errors being accumulated when repeated calculations are done, e.g.

float a = 1.f / 81;
float b = 0;
for (int i = 0; i < 729; ++ i)
    b += a;
printf("%.7g\n", b); // prints 9.000023

while

double a = 1.0 / 81;
double b = 0;
for (int i = 0; i < 729; ++ i)
    b += a;
printf("%.15g\n", b); // prints 8.99999999999996

Also, the maximum value of float is about 3e38, but double is about 1.7e308, so using float can hit "infinity" (i.e. a special floating-point number) much more easily than double for something simple, e.g. computing the factorial of 60.

During testing, maybe a few test cases contain these huge numbers, which may cause your programs to fail if you use floats.

Of course, sometimes, even double isn't accurate enough, hence we sometimes have long double^[1] (the above example gives 9.000000000000000066 on Mac), but all floating point types suffer from round-off errors, so if precision is very important (e.g. money processing) you should use int or a fraction class.

Furthermore, don't use += to sum lots of floating point numbers, as the errors accumulate quickly. If you're using Python, use fsum. Otherwise, try to implement the Kahan summation algorithm.

^{[1]: The C and C++ standards do not specify the representation of float, double and long double. It is possible that all three are implemented as IEEE double-precision. Nevertheless, for most architectures (gcc, MSVC; x86, x64, ARM) float is indeed a IEEE single-precision floating point number (binary32), and double is a IEEE double-precision floating point number (binary64).}

The default choice for a floating-point type should be double. This is also the type that you get with floating-point literals without a suffix or (in C) standard functions that operate on floating point numbers (e.g. exp, sin, etc.).

float should only be used if you need to operate on a lot of floating-point numbers (think in the order of thousands or more) and analysis of the algorithm has shown that the reduced range and accuracy don't pose a problem.

long double can be used if you need more range or accuracy than double, and if it provides this on your target platform.

In summary, float and long double should be reserved for use by the specialists, with double for "every-day" use.

Floating point numbers in C use IEEE 754 encoding.

This type of encoding uses a sign, a significand, and an exponent.

Because of this encoding, many numbers will have small changes to allow them to be stored.

Also, the number of significant digits can change slightly since it is a binary representation, not a decimal one.

Single precision (float) gives you 23 bits of significand, 8 bits of exponent, and 1 sign bit.

Double precision (double) gives you 52 bits of significand, 11 bits of exponent, and 1 sign bit.

The basic types in C are just there to standardize a single unit of memory (a block of bits) that can be used to store a value. We all know that a computer uses bits as its basic unit of information, however a bit is too small to be useful in and of itself, by defining different types we define different blocks of bits and how to interpret them. When we say "int a", the compiler knows that we are dealing with a basic, signed binary number, and knows the amount of memory it needs to set aside to store that number.

The biggest issue is that the exact size definitions are system dependent and not defined in the specifications.

1. A float and double are both implementations of floating point values in C. floating point numbers are a way to implement decimal and fractional values, of any magnitude in binary and also streamline their arithmetic. It is essentially a binary version of scientific notation. Imagine writing the number 3.14159 In decimal, The mantissa here would be 314159 and the exponent would be -5. You could define a simple function that takes the two numbers (stored in binary) and prints out their combined decimal value, your program could therefore store all decimal numbers as two different numbers in binary, and use its own functions to add them together, print them etc. However, C streamlines this process by giving you a simple container that does all that work for you behind the scene. A floating point standard describes how you would encode the mantissa and exponent into a single binary number. In C, the only difference between a float and a double is the amount of memory set aside to store your number, and thus the greater range and precision of the numbers that you can store. The benefit of this is that you can also describe large integer numbers, for instance, you would need 32 bits to write the number "4 billion" explicitly in binary, but you only need 8 to do the same in floating point (4 x 10^9). However, you would not be able to write the number 4,123,456,789 as an 8 bit floating point or even a 32 bit floating point number (as you still need to encode the exponent), but it will fit perfectly well in a 32 bit int.

2. A char and int are just basic binary numbers, their only difference being in length (potentially). A character is defined as the smallest unit of data necessary to hold a single text character for that architecture, this is a bit abstractly defined, but for most computer today running x86 platforms, a char is defined as 8 bits (although, on unicode systems it could be 16 bits). An integer is another basic binary number, but it is required to be at least 16 bits long (typically it is either 32 or 64 on modern systems). So a 8 bit char is capable of encoding 256 unique characters, or a number between 0-255 (or a number between -127 and 128) the difference is only in how you interpret the collection of bits. An 32 bit int can store a number between 0 and slightly over 4 billion, or you could half that range and use it to represent a number between (roughly) -2 billion and 2 billion

On some systems, the size of an int may be the same as the size of float, from the memory point of view they are just collections of bits, however the processor will interpret the values differently, and will actually use different circuits to add two numbers together if they are floats vs if they ints.

The exact value of the closest float to 1.1 is 1.10000002384185791015625. The binary equivalent is 1.00011001100110011001101

The exact value of the closest double to 1.1 is 1.100000000000000088817841970012523233890533447265625. The binary equivalent is 1.0001100110011001100110011001100110011001100110011010.

Lining up the two binary numbers next to each other:

1.00011001100110011001101
1.0001100110011001100110011001100110011001100110011010

The first few truncated bits for rounding to float are 11001100, which is greater than half, so the conversion to float rounded up, making its least significant bits 11001101. That rounding resulted in the most significant difference being a 1 in the float in a bit position that is 0 in the double. The float is greater than the double, regardless of values of bits of lower significance being zero in the float extended to double, but non-zero in the double.