Exploring how to count in alternative number bases to gain a deeper appreciation of our base 10 number system

How we came to have a base 10 number system is a fascinating question. It is interesting for students to appreciate that it is not a “given” that we have a base 10 number system, and that in fact, one can count with number systems of any base. We will discuss the history of our Indo-Arabic numerals (0-9), comparing it to early numeral systems such as Babylonian Cuneiform, Egyptian Hieroglyphics, Chinese characters and Mayan numerals. We will discuss the innovative introduction of the character for 0 as a place holder that allows us to represent very large numbers with ease. We will introduce the concept of counting in alternative bases (i.e., using only digits 0-3, 0-4, etc.). We will extend this to building algebraic polynomial expressions. This helps students gain an understanding of the structure or our base 10 number system. We will use materials to discover the rules for counting and adding in any base and how to translate between alternative bases and our base 10 number system. We will demonstrate the practical use of base 2 (the binary system) as the language of computers. This work can be used as a supplement to any curriculum being used.