Whats the difference between float and numeric in Postgresql?

Reading the Postgresql docs [about the numeric data types](https://www.postgresql.org/docs/12/datatype-numeric.html) leads me to this question: why do I get these unexpected results with the data types Float (SQL standard) and Numeric in Postgresql? For example: CREATE TEMP TABLE testnum (a numeric, b float); INSERT INTO testnum VALUES (100,100); INSERT INTO testnum VALUES (9*9*9,9*9*9); INSERT INTO testnum VALUES (9^9^9,9^9^9); SELECT (a/3)*3 AS numeric, (b/3) * 3 AS float FROM testnum; SELECT (a/5)*5 AS numeric, (b/5) * 5 AS float FROM testnum; Then run SELECT (a/3)*3 AS numeric, (b/3) * 3 AS float FROM testnum; numeric | float 99.9999999999999999 | 100 729.0000000000000000 | 729 In this test Float looks more accurate than Numeric. Which one is the appropriate data type for precise numeric values like currency or inventory quantities?