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A number is called a '''simply normal number to base 10''', if each of of the [[digit]]s {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} appears with the same frequency in its decimal representation. Thus, the number 123,456,789/9,999,999,999 = 0.01234567890123456789... is simply normal.
This concept can be taken to other [[base]]s: 1/3 is not simply normal to base 10, but simply normal to base 2, as its [[dual expansion]] is 0.01010101...<sub>2</sub>.
A ''simply normal number to base 10'' is a ''normal number to base 10'', if not only single digits appear with the frequency of 1/10 in the long run, but each sequence of two digits {00,01,02,... ,98,99} can be found with the frequency of 1/100, each sequence of three digits with a frequency of 1/1000, and in general, each sequence of ''n'' digits will appear with a frequency of approximately 10<sup>-n</sup> when looking up more and more decimal places.
Again, this concept can be taken to other bases.
A number is called '''normal''', if it is normal for every base b.
==See further==
*[https://mathworld.wolfram.com/NormalNumber.html Normal Number] at [[Wolfram Math World]]
This concept can be taken to other [[base]]s: 1/3 is not simply normal to base 10, but simply normal to base 2, as its [[dual expansion]] is 0.01010101...<sub>2</sub>.
A ''simply normal number to base 10'' is a ''normal number to base 10'', if not only single digits appear with the frequency of 1/10 in the long run, but each sequence of two digits {00,01,02,... ,98,99} can be found with the frequency of 1/100, each sequence of three digits with a frequency of 1/1000, and in general, each sequence of ''n'' digits will appear with a frequency of approximately 10<sup>-n</sup> when looking up more and more decimal places.
Again, this concept can be taken to other bases.
A number is called '''normal''', if it is normal for every base b.
==See further==
*[https://mathworld.wolfram.com/NormalNumber.html Normal Number] at [[Wolfram Math World]]