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Most decimal fractions (or most fractions in general) cannot be represented exactly as a fraction with a denominator that is a power of two. For example, the simple decimal fraction 0.3 (3 ⁄ 10) might be represented as 5404319552844595 ⁄ 18014398509481984 (0.299999999999999988897769…). This inexactness causes many problems that are ...
(also written as 0. 9, 0.., or 0.(9)) is a repeating decimal that is an alternative way of writing the number 1. Following the standard rules for representing numbers in decimal notation, its value is the smallest number greater than or equal to every number in the sequence 0.9, 0.99, 0.999, ... .
If a non-repeating set of digits precede the pattern (such as 0.1523 987), one may write the number as the sum of the non-repeating and repeating parts, respectively: 0.1523 + 0.0000 987 Then, convert both parts to fractions, and add them using the methods described above:
The time of day is sometimes represented as a decimal fraction of a day in science and computers. Standard 24-hour time is converted into a fractional day by dividing the number of hours elapsed since midnight by 24 to make a decimal fraction. Thus, midnight is 0.0 day, noon is 0.5 d, etc., which can be added to any type of date, including (all ...
In mathematics, "rational" is often used as a noun abbreviating "rational number". The adjective rational sometimes means that the coefficients are rational numbers. For example, a rational point is a point with rational coordinates (i.e., a point whose coordinates are rational numbers); a rational matrix is a matrix of rational numbers; a rational polynomial may be a polynomial with rational ...
In some contexts it is desirable to round a given number x to a "neat" fraction – that is, the nearest fraction y = m/n whose numerator m and denominator n do not exceed a given maximum. This problem is fairly distinct from that of rounding a value to a fixed number of decimal or binary digits, or to a multiple of a given unit m .
In this example we would multiply by 10 to obtain: = … Now we multiply this equation by 10 r where r is the length of the repetend. This has the effect of moving the decimal point to be in front of the "next" repetend. In our example, multiply by 10 3:
The order of the natural numbers shown on the number line. A number line is a graphical representation of a straight line that serves as spatial representation of numbers, usually graduated like a ruler with a particular origin point representing the number zero and evenly spaced marks in either direction representing integers, imagined to extend infinitely.