Number Theory
# Number Bases

A \(3\)-digit number has digit sum \(15\) and is divisible by \(35\). Find the \(3\)-digit number.

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

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

**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**:

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

Evaluate the following in base 10 :

\[100_2+ 100_{8}+ 100_{10} + 100_{16} \]

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