12/29/2023 0 Comments Infinitesimals 0.999This equality has long been accepted by professional mathematicians and taught in textbooks. In other words: the notations 0.999Ö and 1 actually represent the same real number. In mathematics, the repeating decimal 0.999Ö denotes a real number equal to one. Number precision is a funny thing did you know that an infinitely repeating sequence of 0.999. This problem can show up unexpectedly in the middle of other calculations. If two numbers agree to n figures, you can lose up to n figures of precision in their subtraction. But subtraction can be anywhere from exact to completely inaccurate. As long as you don't overflow or underflow, these operations often produce results that are correct to the last bit. The other elementary operations - addition, multiplication, division - are very accurate. So when are 16 figures not enough? One problem area is subtraction. The charge of an electron is known to 11 significant figures, much more precision than Newton's gravitational constant, but still less than a floating point number. For example, the constant in Newton's Law of Gravity is only known to four significant figures. Hardly any measured quantity is known to anywhere near that much precision. (According to IEEE standard 754, the typical floating point implementation.) Well, numbers are harder to represent on computers than you might think:Ī standard floating point number has roughly 16 decimal places of precision and a maximum value on the order of 10 308, a 1 followed by 308 zeros. What gives? How is it possible to produce such blatantly incorrect results from seemingly trivial calculations? Should we even be trusting our computers to do math at all? However, Excel 2007 displays a result of 100,000.Īt this point, you might be a little perplexed, as computers are supposed to be pretty good at this math stuff. One way to do this is to type "=850*77.1" (without the quotes) into a cell. If you have Excel 2007 installed, try this: Multiply 850 by 77.1 in Excel. On my virtual machine, 12.52 - 12.51 on Ye Olde Windows Calculator indeed results in 0.00. ![]() Press the EQUAL SIGN (=) key on the numeric keypad.Input the smaller number that is one unit lower in the decimal portion (for example, 12.51). ![]() Press the MINUS SIGN (-) key on the numeric keypad.Input the largest number to subtract first (for example, 12.52).Google can't be wrong - math is! But Google is hardly alone this is just another example in a long and storied history of obscure little computer math errors that go way back, such as this bug report from Windows 3.0. You've probably seen this old chestnut by now.
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