1 Evaluate 202 2 three - 112 2 three - WAEC Mathematics 2004 Question
1. Evaluate \( 202^2_{three} - 112^2_{three}\)
A
21120
B
21121
C
21112
D
21011
correct option: a
\(202^2_{three}\)when converted to base ten \(=(202_3)^2\
202_3 = 2 \times 3^2 + 0 \times 3^1 + 2\times 3^0 = 18 + 0 + 2\
=20_{ten}; (202_3)^2 = (20)^2_{ten} = 400\
112^2_{three}\)when converted to base ten \(= (112_3)^2\
112_3 = 1 \times 3^2 + 1 \times 3^1 + 2\times 3^0 = 9+3+2=14_{ten}\
(112_3)^2 = (14)^2_{ten} = 196_{ten}\
Evaluate \Longrightarrow 400-196 = 204\)
Reconvert to base three
\(\begin{matrix}
3 & 204\
3 & 69 &R0\
3 & 22 & R2\
3 & 7 & R1\
2 & 2 & R1\
& 0& R2 \uparrow\
\end{matrix} \
=21120_3\)
202_3 = 2 \times 3^2 + 0 \times 3^1 + 2\times 3^0 = 18 + 0 + 2\
=20_{ten}; (202_3)^2 = (20)^2_{ten} = 400\
112^2_{three}\)when converted to base ten \(= (112_3)^2\
112_3 = 1 \times 3^2 + 1 \times 3^1 + 2\times 3^0 = 9+3+2=14_{ten}\
(112_3)^2 = (14)^2_{ten} = 196_{ten}\
Evaluate \Longrightarrow 400-196 = 204\)
Reconvert to base three
\(\begin{matrix}
3 & 204\
3 & 69 &R0\
3 & 22 & R2\
3 & 7 & R1\
2 & 2 & R1\
& 0& R2 \uparrow\
\end{matrix} \
=21120_3\)
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