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Next whole number after $122_{3}$ in the base three system

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Powers with negative bases

Full solution

Q. Next whole number after

122_{3}

in the base three system

Convert to base ten: Convert $122$ from base three to base ten for easier understanding. $\newline$ $122$ in base three is $1\times3^2 + 2\times3^1 + 2\times3^0 = 9 + 6 + 2 = 17$ in base ten.
Add one for next number: Add $1$ to the base ten number to find the next whole number. $\newline$ $17 + 1 = 18$ in base ten.
Convert back to base three: Convert $18$ back to base three. $\newline$ $18$ divided by $3$ is $6$ with no remainder, $6$ divided by $3$ is $2$ with no remainder, and $2$ divided by $3$ is $0$ with a remainder of $2$ . $\newline$ So, $18$ in base three is written as $18$ $2$ .

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