Leaderboard ad size
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728 × 90. It is a desktop format; it does not fit a phone screen at all, which is why the 320 × 50 mobile leaderboard exists and now carries far more impressions.
How to use the leaderboard ad size
The 8:1 ratio is the design problem: ninety pixels of height is roughly two lines of legible type, so a leaderboard has room for a logo, a short line and a button, and nothing else. Everything about the format pushes toward one clear message. The traffic story is worth knowing too: leaderboards were the dominant display format when browsing was mostly desktop, and mobile has moved most of that volume to 320 × 50 and 320 × 100. If you are building for reach rather than for a specific desktop placement, build the mobile sizes first.
Questions
728 × 90 pixels, under 150 KB.
No, it is too wide. The mobile equivalent is 320 × 50.
A logo, one short line and a button. Anything more is illegible.
970 × 250, a premium above-the-fold desktop placement.
The mobile sizes, unless you have a specific desktop placement in mind. That is where the impressions are.