There’s no 1⁄2 in the 2-adic integers, but there’s a 1⁄2 in the 2-adic numbers where you’re allowed finitely many places after the decimal (binary) point. So although e.g. 1⁄3 = …0101010101 with nothing right of the binary point, 1⁄2 = 0.1 with a single place to the right. So 5⁄6 = …0101010101.1.
There’s no 1⁄2 in the 2-adic integers, but there’s a 1⁄2 in the 2-adic numbers where you’re allowed finitely many places after the decimal (binary) point. So although e.g. 1⁄3 = …0101010101 with nothing right of the binary point, 1⁄2 = 0.1 with a single place to the right. So 5⁄6 = …0101010101.1.