Definition:Non-Recurring Decimal

Definition

A non-recurring decimal is a non-terminating decimal whose decimal expansion does not repeat itself in a recurring pattern.

Examples

Example: $\pi$

The decimal expansion of $\pi$ is non-recurring.

The decimal expansion of $\pi$ starts:

$\pi \approx 3 \cdotp 14159 \, 26535 \, 89793 \, 23846 \, 26433 \, 83279 \, 50288 \, 41971 \ldots$

Example: $\sqrt 2$

The decimal expansion of the square root of $2$ is non-recurring:

$\sqrt 2 \approx 1 \cdotp 41421 \, 35623 \, 73095 \, 04880 \, 16887 \, 24209 \, 69807 \, 85697 \ldots$

Example: $e$

The decimal expansion of Euler's number $e$ is non-recurring.

The decimal expansion of Euler's number $e$ starts:

$2 \cdotp 71828 \, 18284 \, 59045 \, 23536 \, 02874 \, 71352 \, 66249 \, 77572 \, 47093 \, 69995 \ldots$

Also known as

A non-recurring decimal is also known as:

a non-repeating decimal or nonrepeating decimal

a non-periodic decimal or nonperiodic decimal.

Also see

• Definition:Terminating Decimal
• Definition:Non-Terminating Decimal
• Definition:Recurring Decimal

• Results about non-recurring decimals can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): decimal
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): decimal