01-19-2016, 01:47 PM
They are most often used to mean non-repeating non-terminating (irrational), for example pi = 3.14159...
While there are several notational conventions for representing repeating decimals, none of them are accepted universally. In the United States, the convention is generally to indicate a repeating decimal by drawing a horizontal line (a vinculum) above the repetend (\tfrac{1}{3}=0.\overline{3}). In the United Kingdom and mainland China, the convention is to place dots above the outermost numerals of the repetend (\tfrac{1}{3}=0.\dot{3}). Another notation employed in parts of Europe is to enclose the repetend in parentheses (\tfrac{1}{3}=0.(3)). Repeating decimals may also be represented by three periods (an ellipsis, e.g., 0.333…
, although this method introduces uncertainty as to which digits should be repeated or even whether repetition is occurring at all, since such ellipses are also employed for irrational decimals such as 3.14159…
While there are several notational conventions for representing repeating decimals, none of them are accepted universally. In the United States, the convention is generally to indicate a repeating decimal by drawing a horizontal line (a vinculum) above the repetend (\tfrac{1}{3}=0.\overline{3}). In the United Kingdom and mainland China, the convention is to place dots above the outermost numerals of the repetend (\tfrac{1}{3}=0.\dot{3}). Another notation employed in parts of Europe is to enclose the repetend in parentheses (\tfrac{1}{3}=0.(3)). Repeating decimals may also be represented by three periods (an ellipsis, e.g., 0.333…
, although this method introduces uncertainty as to which digits should be repeated or even whether repetition is occurring at all, since such ellipses are also employed for irrational decimals such as 3.14159…
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