Question

how Fibonacci sequence encoded in 1/89​

Answer 1

1/89=0.0112359550561797752808988764

Observe the digits after decimal. They all occur like terms of Fibonacci series. If we tabulate these Fibonacci numbers 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ..in a column, shifting the decimal point one place to the right for each successive number, the sum equals 1/89, as indicated below:

Specifically, think of the Fibonacci series as sequence of decimal fractions, arranged so the right most digit of the (n)th Fibonacci number is in the (n+1)th decimal place and then it's added.