Why is the result of Decimal.MaxValue - 0.5 an integer?

Question

I was playing with decimal today. I noticed this:

Decimal.MaxValue 
79228162514264337593543950335

Decimal.MaxValue - 0.5m
79228162514264337593543950334

The following code prints true.

static void Main(string[] args)
        {
            decimal d = Decimal.MaxValue - 0.5M;
            var b = d % 1 == 0;
            Console.WriteLine(b);

        }

I am sure there is a reason behind this but I don't know what it is.

Answer 1

The decimal type uses 96 bits to store the sequence of digits (ref), plus a sign (1 bit) and a scaling factor that specifies the location of the decimal place.

For this decimal number:

79228162514264337593543950335

All 96 bits are used to the left of the decimal point - there's nothing left to represent the fractional part of the answer. So, it gets rounded.

If you divide the number by 10:

7922816251426433759354395033.5

Then you have a few bits available to represent the fractional part - but only to 1/10, no finer.

The key difference between decimal and double/float is that it is based on a decimal scaling factor specifying the location of a decimal point; the other floating types are based on a binary scaling factor specifying the location of a binary point.

Answer 2

0.5 is being rounded before subtraction. decimal strives to make the result as precise as possible, so the operation becomes 79228162514264337593543950335 - 00000000000000000000000000000.5. But 0.5 cannot be represented as a decimal of the required precision and is rounded upwards to 1.