Because we have ten digits and have learned to count in tens. We use the numbers 0, 1, 2, ..., 9: that is ten different digits.
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9 (base 10) = 1001 (base 2)
It is called the binary system. It uses only 2 numbers. The numbers are "0" and "1" This is a computer language. Base 10 is our regular number system... consisting of 10 numbers from 1-9 including 0
9 ≈ 10^0.9524 lg 9 ≈ 0.9524 (where lg is log to base 10).
9
Base 10 is based on groupings of 10, and the digits are called 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Base 11 is based on groupings of 11, and the digits are called 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and A. A is used instead of 10 to avoid confusion, because it is a single digit, not two digits that actually have the base 10 value of 11. Notice in 10 base 10, you are using 2 digits, a 1 in the tens place and a 0 in the ones place. In base 11, you only need 1 digits, an A, which has the same effective value.