Rom. 3:21 But now the righteousness of God without the law is manifested, being witnessed by the law and the prophets; 22. Even the righteousness of God which is
by faith of Jesus Christ unto all and upon all them that believe: for there is no difference:
The apostle makes it clear that we are not the righteous ones in chapters 1-3, whether Gentile or Jew all are under condemnation. He then goes on to say in verse 21 But now the righteousness of God is manifest through faith, faith in what? The verse is telling us that it is by faith of Jesus and
not by our faith in Jesus. God in no way would impute righteousness to us based on the faith of sinners.
The last part of this verse says this righteousness came upon all them that believe. The word believe is a part of speech called a Synecdoche (pronounced sin-ek-de-key).
It is an exchange by which the whole of something is put for only a part:
Synecdoche is a figure by which one word receives something from another which is internally associated with it by the connection of two ideas: as when a part of a thing is put by a kind of Metonymy for the whole of it, or the whole for a part. The difference between Metonymy and Synecdoche lies in this: that in Metonymy, the exchange is made between two related nouns; while in Synecdoche the exchange is made between two associated ideas.
Some examples from the O.T. and N.T.
Genesis 3:19 (KJV) In the sweat of thy face shalt thou eat bread, till thou return unto the ground; for out of it wast thou taken: for dust thou art, and unto dust shalt thou return.
When the bible uses the term bread it says so because that was a main staple but by no means does it mean that was all they ate.
Jeremiah 26:9b (ESV)
…And all the people gathered around Jeremiah in the house of the LORD.
Not “everyone” did, as is clear from the context, but a large number did. The Synecdoche adds a powerful punch to the verse, as we come face-to-face with the large number of people who rejected God, and Jeremiah His prophet.
Psalms 1:1 (KJV) Blessed is the man that walketh not in the counsel of the ungodly, nor standeth in the way of sinners, nor sitteth in the seat of the scornful.
The synecdoche here is "man" it is understood that all mankind is to be considered and not just men.
Matthew 3:5 (ESV) Then Jerusalem and all Judea and all the region about the Jordan were going out to him [John the Baptist]…
Not “all” the people were going, but a large number were. The Synecdoche gives us a feel for the large numbers of people that responded to John the Baptist.
Acts 10:12 (KJV) Wherein were all manner of four footed beasts of the earth, and wild beasts, and creeping things, and fowls of the air.
When Peter had the vision of all manner of four footed beasts of the earth coming down from heaven on a sheet, it is understood that it was not every single animal, bird, or insect but a representative of them by showing him some beasts.
James 2:15 (KJV) If a brother or sister be naked, and destitute of daily food,
If a brother or sister be naked does not mean without clothes but rather scantly dressed.
In the case of the verse before us in Romans 3, believe is a synecdoche, it takes into account all of what is required for salvation; faith in Christ, repentance, and baptism. God delivered on his promise of sending us a Savior, our wrong deeds are now atoned for by the blood of Jesus making us justified in the sight of God, not by our own merit, but by the righteousness of Jesus Christ.