'Righteousness' in the Bible

So David reigned over all Israel, administering justice and righteousness for all his people.

For there [was no one] in all the house of my father {who were not doomed to death} before my lord the king, but you set your servant among those who eat at your table. Do I have any righteousness any longer except to cry out to the king?"

The LORD rewarded me according to my righteousness: according to the cleanness of my hands hath he recompensed me.

Therefore the LORD hath recompensed me according to my righteousness; according to my cleanness in his eye sight.