I know why decimal can not be represented in floating-point accurately. I also know it will be rounded when convert decimal to floating-point according to IEEE 754.
But, now that the actual floating-point is not accurate, for example decimal 0.1 will be rounded in floating-point:
0,01111111011,1001100110011001100110011001100110011001100110011010
the infinite representation is:
0.000110011001...(infinte 1001)
When we print the 0.1 in decimal, the floating-point representation should be convert to decimal, the question is how the rounded floating-point representation can be rounded "accurately"?
I find a similar question here, @Guffa say:
it's close enough so that when the least significant digits are rounded off to display the value
But I don't understand how the rounding works when converting floating-point back to decimal
I do not know if I have made it clear, but I really want to know why.
Thanks.
