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What the largest number in base eleven?
There would need to be a digit which represents Ten. This would be the largest digit. Any number can be represented in any number-base system, so there is no 'largest number' just largest digit. Base eleven is not commonly used as some of the others (like hexadecimal, which uses letters A-F to represent ten through fifteen). You could use A for ten or maybe you want to use X (like roman numeral ten).
Find a base 7 three digit number which has its digits reversed when expressed in base 9?
5037 = 248 = 3059
Can you represent an eight digit number with a five digit number?
Not in a way that would be generally understood. However, it is possible. An 8-digit number in base 10 can be represented by a 5-digit number in base 32. For example, extending the scheme for labeling digits for base 32, VVVVV32 = 3355443110 Similarly, the 8-digit number 33333333 in base 4 is the 5-digit number 65535 in base 10
What is the sum of the digits of the largest even three digit numbers in base ten which doesn't change when the number is reversed?
Perhaps we are thinking of the number 898? If so, then 8+9+8=25. But I am confused by the use of the plural "numbers", when there is only one largest. If I mistake the question, please rephrase it.
What is 1's complement of decimal 10?
The decimal complement of the number 1 is 8. You can find the complement of any digit by subtracting it from the largest single digit value in the base that you're working in.
