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+--- Thread: College Math - card confusing re: repeating decimals (/Thread-College-Math-card-confusing-re-repeating-decimals)
College Math - card confusing re: repeating decimals - mojine - 01-19-2016
Question 7 of 75
Which of the following is a rational number?
3.245
all of the other choices
3.245245â¦
3.24...
Explanation
All of the other choices. 3.245245... is periodic (AMBIGUOUS), 3.245 terminates, and 3.24... is periodic.(AMBIGUOUS) I thought periodic decimals need a bar over the repetend.
College Math - card confusing re: repeating decimals - wombat777 - 01-19-2016
I believe the three dots mean that the pattern after the decimal is continually repeated.
College Math - card confusing re: repeating decimals - mojine - 01-19-2016
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…