For example, 1 / 3 is represented as a non-terminating decimal as follows
2.
It may come as a surprise that terminating decimal fractions can have repeating expansions in binary.
3.
In the standard decimal representation, almost all real numbers do not have a terminating decimal representation.
4.
The terminating decimal representation is usually preferred, contributing to the misconception that it is the only representation.
5.
Decimal fractions have terminating decimal representations and other fractions have repeating decimal representations, whereas irrational numbers have infinite non-repeating decimal representations.
6.
Since 1 / 3 can't be described as a terminating decimal, we allude to it by describing a sequence of terminating decimals that approaches it.
7.
Since 1 / 3 can't be described as a terminating decimal, we allude to it by describing a sequence of terminating decimals that approaches it.
8.
Informally, non-terminating decimals are easily understood, because it is clear that a real number can be approximated to any required degree of precision by a terminating decimal.
9.
Informally, non-terminating decimals are easily understood, because it is clear that a real number can be approximated to any required degree of precision by a terminating decimal.
10.
From this definition, it is clear that positive integers and positive rational numbers with terminating decimal expansions will have terminating 10-adic expansions that are identical to their decimal expansions.
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