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The above is not limited to subtractions, try = 1 + 1.405*2^(-48) in one cell, Excel rounds the display to 1,00000000000000000000, and = 0.9 + 225179982494413×2^(-51) in another, same display [d] above, different rounding for value and display, violates one of the elementary requirements in Goldberg (1991) [8] who states:
"Instead of using a single floating-point number as approximation for the value of a real variable in the mathematical model under investigation, interval arithmetic acknowledges limited precision by associating with the variable a set of reals as possible values.
"A base is a natural number B whose powers (B multiplied by itself some number of times) are specially designated within a numerical system." [1]: 38 The term is not equivalent to radix, as it applies to all numerical notation systems (not just positional ones with a radix) and most systems of spoken numbers. [1]
In statistics, the 68–95–99.7 rule, also known as the empirical rule, and sometimes abbreviated 3sr or 3 σ, is a shorthand used to remember the percentage of values that lie within an interval estimate in a normal distribution: approximately 68%, 95%, and 99.7% of the values lie within one, two, and three standard deviations of the mean ...
Rather than storing values as a fixed number of bits related to the size of the processor register, these implementations typically use variable-length arrays of digits. Arbitrary precision is used in applications where the speed of arithmetic is not a limiting factor, or where precise results with very large numbers are required.
The second typeface is Myriad Pro; the superscript is about 60% of the original characters, raised by about 44% above the baseline.) A subscript or superscript is a character (such as a number or letter) that is set slightly below or above the normal line of type, respectively. It is usually smaller than the rest of the text.
The most common superscript digits (1, 2, and 3) were included in ISO-8859-1 and were therefore carried over into those code points in the Latin-1 range of Unicode. The remainder were placed along with basic arithmetical symbols, and later some Latin subscripts, in a dedicated block at U+2070 to U+209F.
In the figure, the fraction 1/9000 is displayed in Excel. Although this number has a decimal representation that is an infinite string of ones, Excel displays only the leading 15 figures. In the second line, the number one is added to the fraction, and again Excel displays only 15 figures. In the third line, one is subtracted from the sum using ...