To express the decimal number 99 as a base B number, we need to find the largest power of B that is less than 99. In this case, we want the base B number to be a 2-digit number.
Let's start with B = 2:
99 in base 2 is 1100011, which is a 7-digit number.
Next, try B = 3:
99 in base 3 is 10200, which is a 5-digit number.
Then, try B = 4:
99 in base 4 is 1323, which is a 4-digit number.
Therefore, the smallest positive integer B so that when we express the decimal number 99 as a base B number, we still get a 2-digit number is B = 5.
Find the smallest positive integer B so that when we express the decimal number 99 as a base B number, we still get a 2-digit number.
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