How to use "importance" in a sentence

She had been determined that neither of them would have reason to feel that his importance in her life had diminished

But when Bruckster had come into the hotel thirty minutes ago, Evans had been chatting with the players at his blackjack table, cracking jokes, and grinning as if nothing of any importance had happened in his life lately.

Alexander was proud of the importance of his position

But he was also frustrated because so few people were aware of his great importance.