Decimal Sequence

Decimal Sequence

Name given to the decimal expansion of a real number.

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.