Editing Divisibility rule (section)

====Case where only the last digit(s) are removed====

Most numbers do not divide 9 or 10 evenly, but do divide a higher power of 10<sup>''n''</sup> or 10<sup>''n''</sup>&nbsp;−&nbsp;1. In this case the number is still written in powers of 10, but not fully expanded.

For example, 7 does not divide 9 or 10, but does divide 98, which is close to 100.  Thus, proceed from

: <math>100 \cdot a + b,</math>

where in this case ''a'' is any integer, and ''b'' can range from 0 to 99.  Next,

: <math>(98 + 2) \cdot a + b,</math>

and again expanding

: <math>98 \cdot a + 2 \cdot a + b,</math>

and after eliminating the known multiple of 7, the result is

: <math>2 \cdot a + b,</math>

which is the rule "double the number formed by all but the last two digits, then add the last two digits".