Period of Reciprocal of 729 is 81/Mistake
Jump to navigation
Jump to search
Source Work
1986: David Wells: Curious and Interesting Numbers:
- The Dictionary
- $729$
1997: David Wells: Curious and Interesting Numbers (2nd ed.):
- The Dictionary
- $729$
Mistake
- $1 / 729$ has a decimal period of $81$ digits, which can be arranged in groups of $9$ digits, reading across each row, in this pattern:
\(\ds 001 \, 371 \, 742\) | \(\) | \(\ds \) | ||||||||||||
\(\ds 112 \, 482 \, 853\) | \(\) | \(\ds \) | ||||||||||||
\(\ds 223 \, 593 \, 964\) | \(\) | \(\ds \) | ||||||||||||
\(\ds 334 \, 705 \, 075\) | \(\) | \(\ds \) | ||||||||||||
\(\ds 445 \, 816 \, 186\) | \(\) | \(\ds \) | ||||||||||||
\(\ds 556 \, 927 \, 297\) | \(\) | \(\ds \) | ||||||||||||
\(\ds 668 \, \color {red} 6 38 \, 408\) | \(\) | \(\ds \) | ||||||||||||
\(\ds 779 \, 149 \, 519\) | \(\) | \(\ds \) | ||||||||||||
\(\ds 890 \, 260 \, 631\) | \(\) | \(\ds \) |
The $\color { red } {\text {red} }$ digit is wrong.
Instead of $6$ it should be $0$:
\(\ds 001 \, 371 \, 742\) | \(\) | \(\ds \) | ||||||||||||
\(\ds 112 \, 482 \, 853\) | \(\) | \(\ds \) | ||||||||||||
\(\ds 223 \, 593 \, 964\) | \(\) | \(\ds \) | ||||||||||||
\(\ds 334 \, 705 \, 075\) | \(\) | \(\ds \) | ||||||||||||
\(\ds 445 \, 816 \, 186\) | \(\) | \(\ds \) | ||||||||||||
\(\ds 556 \, 927 \, 297\) | \(\) | \(\ds \) | ||||||||||||
\(\ds 668 \, \color {red} 0 38 \, 408\) | \(\) | \(\ds \) | ||||||||||||
\(\ds 779 \, 149 \, 519\) | \(\) | \(\ds \) | ||||||||||||
\(\ds 890 \, 260 \, 631\) | \(\) | \(\ds \) |
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $729$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $729$