NECO 2024 · Paper 2 · Q6

(a)
Use mathematical tables to evaluate $\dfrac{\sqrt[4]{4000} \times 75.9}{5.61 \times 4.39}$ .
(b)
Express $4553_{\text{six}}$ in base three.

Worked solution (try it first)

The antilog of $.3892$ is 2450, and the characteristic 1 means $\times 10$ : the answer is about $24.50$ .

First change to base ten: $4553_{\text{six}} = 4 \times 216 + 5 \times 36 + 5 \times 6 + 3$
$= 864 + 180 + 30 + 3$
$= 1077$ .
Then divide by 3 repeatedly, keeping the remainders: $1077 \div 3 = 359$ r 0.
$359 \div 3 = 119$ r 2.
$119 \div 3 = 39$ r 2.
$39 \div 3 = 13$ r 0.
$13 \div 3 = 4$ r 1.
$4 \div 3 = 1$ r 1.
$1 \div 3 = 0$ r 1.
Read the remainders from the bottom up: $1110220_{\text{three}}$ .