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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 ...
Rounding or rounding off means replacing a number with an approximate value that has a shorter, simpler, or more explicit representation. For example, replacing $ 23.4476 with $ 23.45, the fraction 312/937 with 1/3, or the expression √2 with 1.414.
Quantile. Probability density of a normal distribution, with quantiles shown. The area below the red curve is the same in the intervals (−∞,Q1), (Q1,Q2), (Q2,Q3), and (Q3,+∞). In statistics and probability, quantiles are cut points dividing the range of a probability distribution into continuous intervals with equal probabilities, or ...
Ceiling function. In mathematics, the floor function is the function that takes as input a real number x, and gives as output the greatest integer less than or equal to x, denoted ⌊x⌋ or floor (x). Similarly, the ceiling function maps x to the least integer greater than or equal to x, denoted ⌈x⌉ or ceil (x). [1]
If x is rational, it will have two continued fraction representations that are finite, x 1 and x 2, and similarly a rational y will have two representations, y 1 and y 2. The coefficients beyond the last in any of these representations should be interpreted as +∞; and the best rational will be one of z(x 1, y 1), z(x 1, y 2), z(x 2, y 1), or ...
Percentile. Statistic which divides a data set into 100 parts and analyzes it as a percentage. In statistics, a k-th percentile, also known as percentile score or centile, is a score below which a given percentage k of scores in its frequency distribution falls (" exclusive " definition) or a score at or below which a given percentage falls ...
Irreducible fraction. An irreducible fraction (or fraction in lowest terms, simplest form or reduced fraction) is a fraction in which the numerator and denominator are integers that have no other common divisors than 1 (and −1, when negative numbers are considered). [1] In other words, a fraction a b is irreducible if and only if a and ...
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 ...