It's a elastic system, there's no fixed proportions like that and that is by design. What you call core money are Federal Reserve Notes(FRN), the other compone

It's a elastic system, there's no fixed proportions like that and that is by design. What you call core money are Federal Reserve Notes(FRN), the other component that you call account balance is called Federal Reserve Credit(FRC), together they make up what's called Monetary Base or base money. Think of monetary base as level one fundamental money. FRN is not better or more "real" than FRC in in any way or vice versa, they're both exactly the same and controlled by the Fed. How much cash is in circulation changes depending on what the public wants, if they demand more cash then Fed decreases credit balance of banks and sends hard cash to their branches to satisfy the demand. If the opposite happens where the banks are holding too much cash, they deposit it back to Fed and fed increases their balance and reduces cash in circulation. In reality though, FRN is miniscule compared to FRC because the vast majority of transactions are settled digitally. Hard to believe now, but in 1913 one of the primary reasons for the Fed's creation was to provide an "elastic currency", which is provide notes to member banks when their customers demand 'hard cash'. The primary concern back then was if a bank failed to furnish cash when it's depositors asked for it, there was a real risk of a bank run driven by panic, even if the bank was in good shape.