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In general, if an increase of x percent is followed by a decrease of x percent, and the initial amount was p, the final amount is p (1 + 0.01 x)(1 − 0.01 x) = p (1 − (0.01 x) 2); hence the net change is an overall decrease by x percent of x percent (the square of the original percent change when expressed as a decimal number).
If the ratio consists of only two values, it can be represented as a fraction, in particular as a decimal fraction. For example, older televisions have a 4:3 aspect ratio, which means that the width is 4/3 of the height (this can also be expressed as 1.33:1 or just 1.33 rounded to two decimal places). More recent widescreen TVs have a 16:9 ...
Also the converse is true: The decimal expansion of a rational number is either finite, or endlessly repeating. Finite decimal representations can also be seen as a special case of infinite repeating decimal representations. For example, 36 ⁄ 25 = 1.44 = 1.4400000...; the endlessly repeated sequence is the one-digit sequence "0".
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
For example, if six bits are used to represent the number "00 1010" (decimal positive 10) and the sign extends operation increases the word length to 16 bits, then the new representation is simply "0000 0000 0000 1010". Thus, both the value and the fact that the value was positive are maintained.
As an example, suppose that 30% of widgets made in a factory are defective. Six months later, 20% of widgets are defective. The percentage change is 20% − 30% / 30% = − 1 / 3 = −33 + 1 / 3 %, while the percentage point change is −10 percentage points.
Write the original number in decimal form. The numbers are written similar to the long division algorithm, and, as in long division, the root will be written on the line above. Now separate the digits into pairs, starting from the decimal point and going both left and right. The decimal point of the root will be above the decimal point of the ...
As an example, a sample with 70 % of R isomer and 30 % of S will have a percent enantiomeric excess of 40. This can also be thought of as a mixture of 40 % pure R with 60 % of a racemic mixture (which contributes half 30 % R and the other half 30 % S to the overall composition).