Decimal numbers have become an increasingly important topic of the elementary and junior high school mathematics curriculum. However, national and state education assessments indicate that students have incomplete and distorted conceptions of decimal numbers. This paper reports initial data from a two-year project designed to elicit and describe students' understanding of decimals. Students in grades 3, 5, 7, and 9 were given written tests and interviewed individually on a variety of decimal tasks. Of primary interest here are tasks that considered decimals as (1) quantities that have value; (2) extensions of whole numbers; and (3) equivalents of common fractions. Results indicate that students perceive decimals primarily as symbols upon which to perform syntactic maneuvers. Although many students have significant hidden understandings, they rarely connect these with the procedural rules they have memorized. (JN)