That would probably be included in the fear of numbers: numerophobia or arithmophobia.
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the number that never ends and never repeats the same format is called non terminating non recurring decimals
It depends on whether they are never ending but recurrent or never ending but non-recurring. An example of the first is 2/11 = 0.1818.... where the 18s go on for ever. This is called a recurring decimal. An example of the second is the decimal representation of sqrt(2) = 1.41421356... which goes on forever, but which does not settle into a repeating pattern. These are called non-recurring decimals.
3.3000, or 3.2999... (recurring).
The question only shows ten places of decimals, then it stops. In the form given in the question it is not a recurring decimal. A recurring decimal continues infinitely. e.g. 1/3 rd expressed as a decimal has an answer of infinite length. Of course, if the question only shows part of the decimal value, and if that value actually extends infinitely, then it is a recurring decimal. Other examples of recurring decimals: 1/7, 1/13, etc. For more comprehensive information about recurring decimals, see 'Related Links' below the following advertisements.
4340.1429