Recurring Decimal/Examples/0.714 285 714...
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Example of Recurring Decimal
The number $\dfrac 5 7$ can be expressed as a recurring decimal:
| \(\ds \dfrac 5 7\) | \(=\) | \(\ds 0 \cdotp 714 \, 285 \, 714 \ldots\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 0 \cdotp \dot 714 \, 28 \dot 5\) | using recurrence notation |
Proof
| \(\ds 0 \cdotp \dot 714 \, 28 \dot 5\) | \(=\) | \(\ds \dfrac {714 \, 285} {999 \, 999}\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \dfrac 5 7\) |
$\blacksquare$
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