Example
The decimal expansion of the rational number \(\frac{1}{7}\) is :\(\frac{1}{7}\) = 0.142 857 142 857 …
Therefore, we can write: \(\frac{1}{7}\) = \(\overline {142\space857}\)
This is a periodic decimal sequence, because the sequence of digits 142 857 repeats infinitely.
Educational Note
We can express a rational number in fractional form a/b or in decimal form. If the decimal sequence that corresponds to this rational number is limited (or finite), this decimal sequence corresponds to a decimal number. If not, the decimal sequence does not correspond to a decimal number.
We often express a rational number as an approximate value rounded to a certain order of magnitude. This approximate value is a decimal number that is an approximation and not an exact value of the rational number in question.
For example, we must avoid saying that \(\frac{1}{3}\) can be expressed by a decimal number. It would be more correct to say that \(\frac{1}{3}\) can be expressed in the form of a decimal expression or a decimal sequence.