Reciprocal of 89

Theorem
The decimal expansion of the reciprocal of $89$ contains the Fibonacci sequence:
 * $\dfrac 1 {89} = 0 \cdotp \dot 01123 \, 59550 \, 56179 \, 77528 \, 08988 \, 76404 \, 49438 \, 20224 \, 719 \dot 1$

Proof
Performing the calculation using long division:

0.0112359550561797752808988764044943820224719101... -- 89)1.0000000000000000000000000000000000000000000000000     89       534       712       801        89     --       ---       ---       ---       ---       110       160       880       390       810      89        89       801       356       801     ---       ---       ---       ---       ---      210       710       790       340        90      178       623       712       267        89      ---       ---       ---       ---        --       320       870       780       730        100       267       801       712       712         89       ---       ---       ---       ---        ---         530       690       680       180       ...        445       623       623       178        ---       ---       ---       ---         850       670       570        200         801       623       534        178         ---       ---       ---        ---          490       470       360        220          445       445       356        178           --       ---       ---        ---           450       250        400       420           445       178        356       356           ---       ---        ---       ---             500      720        440       640             445      712        356       623             ---      ---        ---       ---              550       800       840       170              534       712       801        89