I'm confused in differentiating between these two types of numbers. I'm a newbie.
Can anyone here please explain this?
floating point - Difference between decimal, float and double in .NET? - Stack Overflow
Why do we need to differentiate between float numbers and integers?
Integer vs Float
What is the difference between int and double and how do you know when to use them?
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floatstores floating-point values, that is, values that have potential decimal placesintonly stores integral values, that is, whole numbers
So while both are 32 bits wide, their use (and representation) is quite different. You cannot store 3.141 in an integer, but you can in a float.
Dissecting them both a little further:
In an integer, all bits except the leftmost one are used to store the number value. This is (in Java and many computers too) done in the so-called two's complement, which support negatives values. Two's complement uses the leftmost bit to store the positive (0) or negative sign (1). This basically means that you can represent the values of −231 to 231 − 1.
In a float, those 32 bits are divided between three distinct parts: The sign bit, the exponent and the mantissa. They are laid out as follows:
S EEEEEEEE MMMMMMMMMMMMMMMMMMMMMMM
There is a single bit that determines whether the number is negative or non-negative (zero is neither positive nor negative, but has the sign bit set to zero). Then there are eight bits of an exponent and 23 bits of mantissa. To get a useful number from that, (roughly) the following calculation is performed:
M × 2E
(There is more to it, but this should suffice for the purpose of this discussion)
The mantissa is in essence not much more than a 24-bit integer number. This gets multiplied by 2 to the power of the exponent part, which, roughly, is a number between −128 and 127.
Therefore you can accurately represent all numbers that would fit in a 24-bit integer but the numeric range is also much greater as larger exponents allow for larger values. For example, the maximum value for a float is around 3.4 × 1038 whereas int only allows values up to 2.1 × 109.
But that also means, since 32 bits only have 4.2 × 109 different states (which are all used to represent the values int can store), that at the larger end of float's numeric range the numbers are spaced wider apart (since there cannot be more unique float numbers than there are unique int numbers). You cannot represent some numbers exactly, then. For example, the number 2 × 1012 has a representation in float of 1,999,999,991,808. That might be close to 2,000,000,000,000 but it's not exact. Likewise, adding 1 to that number does not change it because 1 is too small to make a difference in the larger scales float is using there.
Similarly, you can also represent very small numbers (between 0 and 1) in a float but regardless of whether the numbers are very large or very small, float only has a precision of around 6 or 7 decimal digits. If you have large numbers those digits are at the start of the number (e.g. 4.51534 × 1035, which is nothing more than 451534 follows by 30 zeroes – and float cannot tell anything useful about whether those 30 digits are actually zeroes or something else), for very small numbers (e.g. 3.14159 × 10−27) they are at the far end of the number, way beyond the starting digits of 0.0000...
Floats are used to store a wider range of number than can be fit in an integer. These include decimal numbers and scientific notation style numbers that can be bigger values than can fit in 32 bits. Here's the deep dive into them: http://en.wikipedia.org/wiki/Floating_point
float (the C# alias for System.Single) and double (the C# alias for System.Double) are floating binary point types. float is 32-bit; double is 64-bit. In other words, they represent a number like this:
10001.10010110011
The binary number and the location of the binary point are both encoded within the value.
decimal (the C# alias for System.Decimal) is a floating decimal point type. In other words, they represent a number like this:
12345.65789
Again, the number and the location of the decimal point are both encoded within the value – that's what makes decimal still a floating point type instead of a fixed point type.
The important thing to note is that humans are used to representing non-integers in a decimal form, and expect exact results in decimal representations; not all decimal numbers are exactly representable in binary floating point – 0.1, for example – so if you use a binary floating point value you'll actually get an approximation to 0.1. You'll still get approximations when using a floating decimal point as well – the result of dividing 1 by 3 can't be exactly represented, for example.
As for what to use when:
For values which are "naturally exact decimals" it's good to use
decimal. This is usually suitable for any concepts invented by humans: financial values are the most obvious example, but there are others too. Consider the score given to divers or ice skaters, for example.For values which are more artefacts of nature which can't really be measured exactly anyway,
float/doubleare more appropriate. For example, scientific data would usually be represented in this form. Here, the original values won't be "decimally accurate" to start with, so it's not important for the expected results to maintain the "decimal accuracy". Floating binary point types are much faster to work with than decimals.
Precision is the main difference.
Float - 7 digits (32 bit)
Double-15-16 digits (64 bit)
Decimal -28-29 significant digits (128 bit)
Decimals have much higher precision and are usually used within financial applications that require a high degree of accuracy. Decimals are much slower (up to 20X times in some tests) than a double/float.
Decimals and Floats/Doubles cannot be compared without a cast whereas Floats and Doubles can. Decimals also allow the encoding or trailing zeros.
float flt = 1F/3;
double dbl = 1D/3;
decimal dcm = 1M/3;
Console.WriteLine("float: {0} double: {1} decimal: {2}", flt, dbl, dcm);
Result :
float: 0.3333333
double: 0.333333333333333
decimal: 0.3333333333333333333333333333
Hi all. Im a complete beginner learning the basics. Im curious as to why Python has two different types of numbers (3 including complex) : Floats and integers. Why cant we just use any number and if we do wanna use a decimal point, we just use a decimal point without having to indicate it as a float? What is the significance of differentiating the two? Thanks!