Example
The
decimal expansion of the rational number [latex]\frac{1}{7}[/latex] is :[latex]\frac{1}{7}[/latex] = 0.142 857 142 857 ...
Therefore, we can write: [latex]\frac{1}{7}[/latex] = [latex]\overline {142\space857}[/latex]
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 [latex]\frac{1}{3}[/latex] can be expressed by a decimal number. It would be more correct to say that [latex]\frac{1}{3}[/latex] can be expressed in the form of a decimal expression or a decimal sequence.
