Decimal Notation

The Roman numeral above is not a correct representation of an integer. But it takes some inspection to decide this. Decimal positional representation is clearly better.

You already know how decimal notation works (and probably would be happy to skip this topic).

324 means:  3 × 100  +  2 × 10  +  4 × 1 

which is:   3 × 102  +  2 × 101 +  4 × 100

Remember that:

B0   =  1,  no matter what number B is.

Rules for Positional Notation.

1. The base B is (usually) a positive integer.
2. There are B "digits" representing zero up to (B minus one).
3. Positions correspond to integer powers of B, starting with power zero, and increasing right to left.
4. The digit placed at a position shows how many times that power of B is included in the number.