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Excel maintains 15 figures in its numbers, but they are not always accurate; mathematically, the bottom line should be the same as the top line, in 'fp-math' the step '1 + 1/9000' leads to a rounding up as the first bit of the 14 bit tail '10111000110010' of the mantissa falling off the table when adding 1 is a '1', this up-rounding is not undone when subtracting the 1 again, since there is no ...
Thus, in the case of 1.0, there are two significant figures, whereas 1 (without a decimal) has one significant figure. Among a number's significant digits, the most significant digit is the one with the greatest exponent value (the leftmost significant digit/figure), while the least significant digit is the one with the lowest exponent value ...
1.3 Operations on two known limits. ... [1] [2] This applies even in the cases that f(x) and g(x) take on different values at c, or are discontinuous at c.
Each standard deviation represents a fixed percentile. Thus, rounding to two decimal places, −3σ is the 0.13th percentile, −2σ the 2.28th percentile, −1σ the 15.87th percentile, 0σ the 50th percentile (both the mean and median of the distribution), +1σ the 84.13th percentile, +2σ the 97.72nd percentile, and +3σ the 99
Because the sum in the second line has only eleven 1's after the decimal, the difference when 1 is subtracted from this displayed value is three 0's followed by a string of eleven 1's. However, the difference reported by Excel in the third line is three 0's followed by a string of thirteen 1's and two extra erroneous digits. This is because ...
For example, 1.6 would be rounded to 1 with probability 0.4 and to 2 with probability 0.6. Stochastic rounding can be accurate in a way that a rounding function can never be. For example, suppose one started with 0 and added 0.3 to that one hundred times while rounding the running total between every addition.
The introduction of Lotus 1-2-3 in November 1982 accelerated the acceptance of the IBM Personal Computer. It was written especially for IBM PC DOS and had improvements in speed and graphics compared to VisiCalc on the Apple II, this helped it grow in popularity. [36] Lotus 1-2-3 was the leading spreadsheet for several years.
The two sequences {Τ 2n−1} and {Τ 2n} might themselves define two convergent continued fractions that have two different values, x odd and x even. In this case the continued fraction defined by the sequence { Τ n } diverges by oscillation between two distinct limit points.