A researcher wants to construct a histogram for a dataset containing $n = 800$ observations. The range of the dataset is $150$ units. According to Sturges' rule, the optimal number of bins $k$ is given by $k = 1 + 3.322 \\log_{10}(n)$. If $k$ is rounded to the nearest integer, what is the resulting bin width $w$ of the histogram (rounded to one decimal place)?