According to Moses, God promised to rewrite the special rules on new stones after Moses broke the first set, and these new stones must be placed in a special box called the Ark. This shows that even when mistakes happen, God can give second chances.
Deuteronomy 10:2: And I will write on the tables the words that were in the first tables which thou brakest, and thou shalt put them in the ark.
Deuteronomy 10:2 states that God will write on the new tablets, whereas in Exodus 34:1, God instructs Moses to write upon the tablets.
Exodus 34:1: And the LORD said unto Moses, Hew thee two tables of stone like unto the first: and I will write upon [these] tables the words that were in the first tables, which thou brakest.