Number Theory

Number Bases

Number Bases: Level 1 Challenges

         

A 33-digit number has digit sum 1515 and is divisible by 3535. Find the 33-digit number.

Convert the following number from base 3 to base 9: 1212121212123\huge{121212121212_3}

1111111111111111(2)+1010101010101010(2)= ? 1111111111111111_{(2)} + 1010101010101010_{(2)} = \ ?

Clarification: The two numbers given are written in base 2, while the numbers in the answer choices are written in base 16.

True or false:

\quad 0.1111112=1\large 0.{111111\ldots}_2 = 1.

Evaluate the following in base 10 :

1002+1008+10010+10016100_2+ 100_{8}+ 100_{10} + 100_{16}

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