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Answer for the clue "Ten at heart of it, my cadet smiles, enigmatically ", 14 letters:
decimal system

Word definitions for decimal system in dictionaries

Wiktionary Word definitions in Wiktionary
n. (context mathematics English) A numerical system of counting in tens using decimal digits.

Wikipedia Word definitions in Wikipedia
Decimal system may refer to: The decimal (base ten) number system, used in mathematics for writing numbers and performing arithmetic. The Dewey Decimal System , a subject classification system used in libraries. The decimal currency system, where each unit ...

WordNet Word definitions in WordNet
n. a positional system of numeration that uses decimal digits and a base of 10 [syn: decimal numeration system , decimal number system ]

Usage examples of decimal system.

True, the decimal system has a similar situation in regard to powers of 10.

The ancient Indo-Europeans, our ancestors, used that same base twelve system for many thousands of years, and used it for their own systems of measurements, until some dull person started to count on his fingers and invented the decimal system in the process.

Karla lapsed into a discussion of the Dewey decimal system and the Library of Congress cataloging system, which was numbing to say the least.

The Dewey Decimal System, devised by Melvil Dewey, is a way of shelving books in libraries.