Interesting pattern in the decimal expansion of 1243There appears to be an interesting pattern in the decimal expansion of12431243=0.004115226337448559670781893―I was wondering if anyone could clarify how this comes about?

1243=1333+1089911333=.003―18991=.000111222333444555666777889―=111998001=111106−2⋅103+1

Expert answers to "Interesting pattern in the decimal expansion of 1243There..."

Jaidyn Cook

2022-04-23

Interesting pattern in the decimal expansion of

\frac{1}{243}

There appears to be an interesting pattern in the decimal expansion of

\frac{1}{243}

\frac{1}{243} = 0 . \overset{―}{004115226337448559670781893}

I was wondering if anyone could clarify how this comes about?

diehaterzh8s

Beginner2022-04-24Added 11 answers

\frac{1}{243} = \frac{1}{333} + \frac{10}{8991}

\frac{1}{333} = . \overset{―}{003}

\frac{1}{8991} = . \overset{―}{000111222333444555666777889} = \frac{111}{998001} = \frac{111}{10^{6} - 2 \cdot 10^{3} + 1}

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