Shortest decimal expansion within binary interval Consider an interval $[x-2^n,x+2^n]$ defined by a binary float $x$ and a power of two $2^n$ typically much smaller than $x$. I would like to know whether an efficient algorithm exists to determine the shortest decimal expansion within the interval. What is the basic idea of such an algorithm? Perhaps such an algorithm has already been published?

In my own search, I have come across the work of Steele &amp; White “How to print floating-point numbers accurately”, but it is not clear to me whether it applies in the sense that their results can be adapted to this particular case.
Decimal numbers with k digits to the right of the decimal point are $10^{-k}$ apart. So if you choose k large enough that $10^{-k} &lt; 2·2^n$, then there is a decimal number with k decimals inside the interval. You can for example calculate it as $round (x·10^k) / 10^k$. 

You may be lucky, and a number with fewer decimals may be inside the interval. Rounding the result to k-1 or fewer decimals may give a result in that interval.