Definition:Recurring Decimal
(Redirected from Definition:Periodic Decimal)
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Definition
A recurring decimal is a non-terminating decimal whose decimal expansion ends with a finite number of digits which repeats itself ad infinitum.
Examples
Example: $0 \cdotp 333 \ldots$
The number $\dfrac 1 3$ can be expressed as a terminating decimal:
| \(\ds \dfrac 1 3\) | \(=\) | \(\ds 0 \cdotp 333 \ldots\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 0 \cdotp \dot 3\) | using recurrence notation |
This would be voiced:
- nought point three recurring
or:
- zero point three recurring
and so on.
Example: $0 \cdotp 714 \, 285 \, 714 \ldots$
The number $\dfrac 5 7$ can be expressed as a terminating decimal:
| \(\ds \dfrac 5 7\) | \(=\) | \(\ds 0 \cdotp 714 \, 285 \, 714 \ldots\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 0 \cdotp \dot 714 \, 28 \dot 5\) | using recurrence notation |
Also known as
A recurring decimal is also known as:
Also see
- Results about 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