what is the meaning of ternimal and non ternimal decimal
Answers
Answer:
Step-by-step explanation:
As proven a few millennia ago (by some Greek mathematician whose name I cannot recall at the moment), that the ratio between two natural numbers {1,2,3,4,5,6,7,…} always has a repeating sequence of digits, when its value is expressed as a decimal number (or as a number another integer base).
If the repeating sequence of digits is all zeroes, it is called “terminating”.
Note that a number is considered “rational” if and only if its value is exactly equal to the ratio between two whole numbers (“integers”); otherwise (if it cannot be equal to the ratio between two integers) it is called “irrational”. Examples of “irrational” numbers (which have no repeating sequences — neither terminal nor nonterminal!) include the square root of of numbers that are not “perfect squares (such as 2 or 3 or 5 or 6), as well as PI and e (the base of natural logarithms), as well as an uncountable number of nonterminating decimal values (such as those representing the (denser infinitude of) points on a line (or, perhaps, the even-denser number of geometric curves!)
However, a repeating sequence of digits that is composed entirely of zeroes is called a “terminating” sequence — because it adds nothing to the value when the infinite series of zeroes is ignored.
Terminating decimals are those numbers which come to an end after few repetitions after decimal point.
A non-terminating, non-repeating decimal is a decimal number that continues endlessly, with no group of digits repeating endlessly.
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