'Righteousness' in the Bible

David reigned over all of Israel, and he was 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?"

Yahweh rewarded me according to my righteousness, according to the cleanness of my hands he recompensed me.

Yahweh has recompensed me according to my righteousness, according to my cleanness before his eyes.