Fibonacci's golden shortcut: how miles leap to kilometres

Abstract The conversion between miles and kilometres can be surprisingly approached using the Fibonacci sequence and the golden ratio. This paper explores a method that leverages Zeckendorf's representation – the expression of any positive integer as a sum of distinct, non-consecutive Fibonacci numbers – to convert any given number of miles to kilometres, or vice versa. We delve into the precision of this "Fibonacci shortcut", deriving explicit lower and upper bounds for the signed relative errors for both conversion directions.