A flippable number consists entirely of digits that have a clean rotational counterpart when the number is rotated 180°. The digits 0, 1, and 8 rotate to themselves; 6 and 9 rotate to each other; the rest (2, 3, 4, 5, 7) have no clean rotation.
Flipping is an involution: flip(flip(n)) = n. When the rotated value equals the original, the number is strobogrammatic (e.g., 88, 1881, 96 with 6/9 viewed in mirror).
When the rotated value differs, you get pairs: 16 ↔ 91, 19 ↔ 61, 109 ↔ 601, 198 ↔ 861. The most well-known flippable amusements come from calculator culture — 5318008 rotates to BOOBIES in seven-segment display, and 0.7734 reads hELLO upside down.