Recurring Decimal/Examples/0.714 285 714...

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
This article is issued from ProofWiki. The text is available under Creative Commons Attribution-ShareAlike License unless otherwise noted. Additional terms may apply for the media files.