Noah believed Gods warning about the coming rain, built his ark and survived the flood. Afterwards, he built an altar and offered burnt offerings upon it. Then Noah built an altar to the LORD, and took of every clean animal and of every clean bird, and offered burnt-offerings on the altar. And the LORD smelled a soothing aroma. Then the LORD said in His heart, "I will never again curse the ground for man's sake” (Gen 8:20). Noah is a picture of a “saved” man; a man delivered from judgment. All flesh upon the earth apart from Noah, his family, and some clean animals were destroyed. Because Noah was delivered from the judgment of God he makes an altar because he had experienced God’s mercy. God revealed Himself to Abraham so he made an altar to God (Genesis 12.1). The Lord delivered Moses from the enemy so Moses built an altar in recognition of Gods help and mercy. (Exodus 17.1)Able, Gideon, Joshua and David all experienced the mercy of God and then built altars to the Lord.
Worship is a recognition that God has manifested His mercy to us; that we have been partakers of His love and delivered from our enemies. Their worship and their sacrifices were acceptable to God because they were offered because of their experience of the mercy of God. Today the only acceptable altar on which we can offer our sacrifice is a revelation of the mercy of God. I beseech you, therefore, brethren, by the mercies of God, that you present your bodies a living sacrifice, holy, acceptable to God, which is your reasonable service. (Rom. 12:1). The “therefore” is the conclusion of what preceded in Romans three to ten. In Romans three it tells us God saves us and we are justified from sin as Able was. Romans five tells us we have peace from God as Gideon had. Romans six tells us we are told we are now alive to God like Noah was alive after the flood. In Romans eight, we are told there is now no condemnation to those in Christ Jesus and Romans nine says that the Gentiles have received mercy and been grafted into God's purposes like Abraham. All these Old Testament men had received mercy and then worshipped God. Therefore in Romans twelve Paul says because you also have experienced God’s mercy like Able, Gideon, and Abraham, present a sacrifice! Our body - a living sacrifice, which is your reasonable service or worship.
Friend, devoting ourselves entirely in worship that stems from a revelation of the mercy of God, will always be acceptable worship to our God and Saviour.