Timeline for What causes floating point rounding errors?

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Feb 25, 2015 at 20:11	comment	added	David Zhang		In particular, the fractions we can express as finite decimals are those whose denominators' prime factorization contains only 2 and 5 (e.g. we can express 3/10 and 7/25, but not 11/18). When we move to binary, we lose the factor of 5, so that only the dyadic rationals (e.g. 1/4, 3/128) can be expressed exactly.
Jan 27, 2015 at 5:35	comment	added	Abhi Beckert		Floating points aren't just useful for a lot of decimal places. 32 bit integers can only count up to about 4 billion, but a 32 bit float can be almost infinitely large.
S Jan 27, 2015 at 5:27	history	suggested	User	CC BY-SA 3.0	Fixed some grammar mistakes
Jan 27, 2015 at 2:42	review	Suggested edits
S Jan 27, 2015 at 5:27
Mar 4, 2013 at 13:39	comment	added	anon		Spot on. But I would also note that some numbers that terminate in decimal don't terminate in binary. In particular 0.1 is a recurring number in binary and so no floating point binary number can exactly represent 0.1.
Aug 17, 2011 at 2:23	vote	accept	nmat
Aug 15, 2011 at 13:34	history	edited	thorsten müller	CC BY-SA 3.0	added 19 characters in body
Aug 15, 2011 at 13:26	history	edited	thorsten müller	CC BY-SA 3.0	added 833 characters in body
Aug 15, 2011 at 13:16	history	answered	thorsten müller	CC BY-SA 3.0