A number is said to be simply normal to base b if its base-b expansion has each digit appearing with average frequency tending to b^(-1). A normal number is an irrational number for which any finite pattern of numbers occurs with the expected limiting frequency in the expansion in a given base (or all bases). For example, for a normal decimal number, each digit 0-9 would be expected to occur 1/10 of the time, each pair of digits 00-99 would be expected to occur 1/100 of the time, etc. A number that is normal in base-b is often called b-normal. A number that is b-normal for every b = 2, 3, ... is said to be absolutely normal.

absolutely normal | binary Champernowne constant | Champernowne constant | Copeland-Erdős constant | e | equidistributed sequence | pi | Stoneham number