Wikipedia
A unit of account in economics is a nominal monetary unit of measure or currency used to value/cost goods, services, assets, liabilities, income, expenses; i.e., any economic item. It is one of three well-known functions of money. It lends meaning to profits, losses, liability, or assets.
A unit of account in financial accounting refers to the words that are used to describe the specific assets and liabilities that are reported in financial statements rather than the units used to measure them.
Unit of account and unit of measure are sometimes treated as synonyms in financial accounting and economics.
The unit of account in economics (unit of measure in accounting) suffers from the pitfall of not being stable in real value over time because money is generally not perfectly stable in real value during inflation and deflation. Inflation destroys the assumption that the real value of the unit of account is stable which is the basis of classic accountancy. In such circumstances, historical values registered in accountancy books become heterogeneous amounts measured in different units. The use of such data under traditional accounting methods without previous correction often leads to invalid results.
All monetary units of measure, e.g., US Dollar, Euro, Yen, Yuan, Ruble, Peso, etc., - all fiat currency units - are assumed to be perfectly stable in real value during non-hyperinflationary conditions under traditional Historical Cost Accounting in terms of which the stable measuring unit assumption is applied. The Daily Consumer Price Index (Daily CPI) - or a monetized daily indexed unit of account - is generally used to index monetary values on a daily basis when it is required to maintain the purchasing power or real value of monetary values constant during inflation and deflation.