Writing down your key is not a good idea as even one "typo" would cause your entire "key" (it wouldn't actually be a key anymore) worthless
Actually, a private key is just a big number (up to 2^256, or more correctly 0xFFFF FFFF FFFF FFFF FFFF FFFF FFFF FFFE BAAE DCE6 AF48 A03B BFD2 5E8C D036 4141).
So with a typo, you would get another valid key, which statistically speaking should be almost sure to be associated with an empty address.