C182 pilot reported fuel starvation during initial approach resulting in an engine out landing.

Narrative

I suffered a fuel starvation event during vectors to final at ZZZ. Our 182 has tip tank extensions which means we have to estimate on fuel but I estimated 40 gallons using 20 to get from ZZZ1 to ZZZ. We had a 15 kt. headwind. As I am being vectored to final my digital gauge is showing 14 gallons left. I had 11 in the left tank and 3 in the right tank and I was flying with left tank selected. I was being vectored to XXL but right as I was crossing over the final approach end of XXL my engine sputtered and I know it was fuel starvation. With lots of jet traffic and knowing I had a landing spot on the XXs I did not try to do a restart and [advised ATC] and turned towards the XX runways. Approach turned me to Tower and I was cleared for a XXL landing where I landed engine out.The emergency team came out and helped me push to Pad XX where a fuel truck came and gave us fuel. We then taxi to FBO. At time of fuel cutoff; my airplane was telling me I had 14 gallons left; 11 in left tank; and I was switched on the left tank.