 Zeroes Table

A Zeroes Table is created by recording identical quantities in different bases on the same row. The columns in this table then represent identical base values.  When the least significant place (the one’s place) is zero in a given row and column then, and only then, is this quantity called a ‘zero’. A ‘zero’ indicates that the quantity is perfectly divisible by the base leaving no remainders. For example, fifteen in base five is three zero. Since the least significant place is zero then fifteen is a zero in-based five and, in fact, fifteen divided by five is three.

When the two least significant places are both zero then it means that the quantity is divisible by the base squared. For example, seventy-two base six is two-zero-zero, and in fact, seventy-two divided by six is two 62’s.

Comparing BNS enables the discovery of factors & multiples.  These are readily apparent when there are zero 1's units (i.e. no remainders).  E.g. 63A is 709 and 1207 defining 9 and 7 as factors of 63.

The preferred exercise is to work with a specific quantity across the base tables 2 to A recording the subquanned value and highlighting the zeroes.  The Excel spreadsheet is for comparative use by a teacher or parent.  Viewing this table prematurely may prevent the enjoyable experience of discovery being realized.  CAUTION