After experiencing distress, David resolves not to speak in front of certain wicked people (Psalms 39:1-3). Rather than holding in his anger, he prays to God. David's question here is not about knowing the exact time or nature of his death. Instead, he is asking God to help him with humility.
As much as we pray and believe God will give us a long life, we must also be careful to live soberly, taking into consideration who we are. We are only pilgrims on this journey. The world is not our home, and we must live with that consciousness every day. It is not a mindset of fear of death but one of reverence for God, who holds our lives in His hands.
Learn the brevity of your life, and you will know how to do better with every fleeting second. Learn your insufficiency in yourself, and you will humble yourself before God for grace and mercy. Our lives are fleeting, and no invention has been able to give us an accurate time of death. Therefore, you are to make use of every minute by redeeming the time and doing all that God counts worthy.

Dear Heavenly Father, I kneel before Your throne of grace. I come to You in my unworthiness and pride. I come to You without any resistance to Your verdict on the wickedness of my heart. Search me, Lord, and try my ways. Find the foolishness in me and correct me. Give me a clearer perspective on life and my purpose on earth. Teach me to know how fleeting my life is, that I may depend on You with all my heart. Teach me to desire the path of life and godliness now and always. 
In Jesus's name I pray. Amen.