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Because pairs of numbers that are aligned on the logarithmic scales form constant ratios, no matter how the scales are offset, slide rules can be used to generate equivalent fractions that solve proportion and percent problems. For example, setting 7.5 on one scale over 10 on the other scale, the user can see that at the same time 1.5 is over 2 ...
Sometimes the − is used to indicate a better grade if it stands after the grade and a lower grade if it stands before the grade (in which case − is a symbol for "bis", e.g. 'to', rather than 'minus'), for example −5 (4.75) is lower than 5 which is lower than 5− (5.25) in that system. In some regions, decimal grades are used: 5.5, 4.5, etc.
For example, 21, 4, 0, and −2048 are integers, while 9.75, 5 + 1 / 2 , 5/4, and √ 2 are not. [8] The integers form the smallest group and the smallest ring containing the natural numbers. In algebraic number theory, the integers are sometimes qualified as rational integers to distinguish them from the more general algebraic integers.
An example of the second case is the decidability of the first-order theory of the real numbers, a problem of pure mathematics that was proved true by Alfred Tarski, with an algorithm that is impossible to implement because of a computational complexity that is much too high. [122]
For percentage grades, 0% is awarded for extremely poor performance and 100% is awarded for exceptional work. The grade of 10 is reserved for exceptional achievements. 9 is most commonly used for a United States equivalent of an A. In some cases, the grade can be rounded for example if a student got 67% the grade can sometimes be rounded to a 7.
Hexadecimal (also known as base-16 or simply hex) is a positional numeral system that represents numbers using a radix (base) of sixteen. Unlike the decimal system representing numbers using ten symbols, hexadecimal uses sixteen distinct symbols, most often the symbols "0"–"9" to represent values 0 to 9 and "A"–"F" to represent values from ten to fifteen.
As another example, a two-year return of 10% converts to an annualized rate of return of 4.88% = ((1+0.1) (12/24) − 1), assuming reinvestment at the end of the first year. In other words, the geometric average return per year is 4.88%. In the cash flow example below, the dollar returns for the four years add up to $265.
The Hatter's hat shows an example of the old pre-decimal notation: the hat costs 10/6 (ten shillings and sixpence, a half guinea). Before decimalisation in 1971, the pound was divided into 20 shillings, and each shilling into 12 pence, making 240 pence to the pound. The symbol for the shilling was "s."
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