Praktis Kendiri 2.1a (Soalan 8 & 9) - Buku Teks Matematik Tingkatan 4 Bab 2 (Asas Nombor)

Soalan 8:
Hitung hasil tambah nilai digit 8 dan nilai digit 3 dalam nombor 1823₉.

Penyelesaian:

1823_{9} = (1 \times 9^{3}) + (8 \times 9^{2}) + (2 \times 9^{1}) + (3 \times 9^{0})

$1823_9=\left(1 \times 9^3\right)+\left(8 \times 9^2\right)+\left(2 \times 9^1\right)+\left(3 \times 9^0\right)$

\begin{matrix} Hasil tambah nilai digit 8 dan nilai digit 3 \begin{matrix} = (8 \times 9^{2}) + (3 \times 9^{0}) = 648 + 3 = 651 \end{matrix} \end{matrix}

$\begin{aligned} &\text { Hasil tambah nilai digit } 8 \text { dan nilai digit } 3\\ &\begin{aligned} & =\left(8 \times 9^2\right)+\left(3 \times 9^0\right) \\ & =648+3 \\ & =651 \end{aligned} \end{aligned}$

Soalan 9:
Susun nombor berikut mengikut urutan menaik.

(a) 110_{2}, 1101_{2}, 111_{2}, 1110_{2}

$\text { (a) } 110_2, 1101_2, 111_2, 1110_2$

(b) 1123_{4}, 132_{4}, 231_{4}, 112_{4}

$\text { (b) } 1123_4, 132_4, 231_4, 112_4$

(c) 324_{5}, 124_{5}, 241_{5}, 231_{5}

$\text { (c) } 324_5, 124_5, 241_5, 231_5$

Penyelesaian:
(a)

\begin{matrix} 110_{2} & = (1 \times 2^{2}) + (1 \times 2^{1}) + (0 \times 2^{0}) = 4 + 2 = 6 \end{matrix}

$\begin{aligned} 110_2 & =\left(1 \times 2^2\right)+\left(1 \times 2^1\right)+\left(0 \times 2^0\right) \\ & =4+2 \\ & =6 \end{aligned}$

\begin{matrix} 1101_{2} & = (1 \times 2^{3}) + (1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0}) = 8 + 4 + 0 + 1 = 13 \end{matrix}

$\begin{aligned} 1101_2 & =\left(1 \times 2^3\right)+\left(1 \times 2^2\right)+\left(0 \times 2^1\right)+\left(1 \times 2^0\right) \\ & =8+4+0+1 \\ & =13 \end{aligned}$

\begin{matrix} 111_{2} & = (1 \times 2^{2}) + (1 \times 2^{1}) + (1 \times 2^{0}) = 4 + 2 + 1 = 7 \end{matrix}

$\begin{aligned} 111_2 & =\left(1 \times 2^2\right)+\left(1 \times 2^1\right)+\left(1 \times 2^0\right) \\ & =4+2+1 \\ & =7 \end{aligned}$

\begin{matrix} 1110_{2} & = (1 \times 2^{3}) + (1 \times 2^{2}) + (1 \times 2^{1}) + (0 \times 2^{0}) = 8 + 4 + 2 + 0 = 14 \end{matrix}

$\begin{aligned} 1110_2 & =\left(1 \times 2^3\right)+\left(1 \times 2^2\right)+\left(1 \times 2^1\right)+\left(0 \times 2^0\right) \\ & =8+4+2+0 \\ & =14 \end{aligned}$

Susun nombor mengikut urutan menaik = 110_{2}, 111_{2}, 1101_{2}, 1110_{2}

$\text { Susun nombor mengikut urutan menaik }=110_2, 111_2, 1101_2, 1110_2$

(b)

\begin{matrix} 1123_{4} & = (1 \times 4^{3}) + (1 \times 4^{2}) + (2 \times 4^{1}) + (3 \times 4^{0}) = 64 + 16 + 8 + 3 = 91 \end{matrix}

$\begin{aligned} 1123_4 & =\left(1 \times 4^3\right)+\left(1 \times 4^2\right)+\left(2 \times 4^1\right)+\left(3 \times 4^0\right) \\ & =64+16+8+3 \\ & =91 \end{aligned}$

\begin{matrix} 132_{4} & = (1 \times 4^{2}) + (3 \times 4^{1}) + (2 \times 4^{0}) = 16 + 12 + 2 = 30 \end{matrix}

$\begin{aligned} 132_4 & =\left(1 \times 4^2\right)+\left(3 \times 4^1\right)+\left(2 \times 4^0\right) \\ & =16+12+2 \\ & =30 \end{aligned}$

\begin{matrix} 231_{4} & = (2 \times 4^{2}) + (3 \times 4^{1}) + (1 \times 4^{0}) = 32 + 12 + 1 = 45 \end{matrix}

$\begin{aligned} 231_4 & =\left(2 \times 4^2\right)+\left(3 \times 4^1\right)+\left(1 \times 4^0\right) \\ & =32+12+1 \\ & =45 \end{aligned}$

\begin{matrix} 112_{4} & = (1 \times 4^{2}) + (1 \times 4^{1}) + (2 \times 4^{0}) = 16 + 4 + 2 = 22 \end{matrix}

$\begin{aligned} 112_4 & =\left(1 \times 4^2\right)+\left(1 \times 4^1\right)+\left(2 \times 4^0\right) \\ & =16+4+2 \\ & =22 \end{aligned}$

Susun nombor mengikut urutan menaik = 112_{4}, 132_{4}, 231_{4}, 1123_{4}

$\text { Susun nombor mengikut urutan menaik }=112_4, 132_4, 231_4, 1123_4$

(c)

\begin{matrix} 324_{5} & = (3 \times 5^{2}) + (2 \times 5^{1}) + (4 \times 5^{0}) = 75 + 10 + 4 = 89 \end{matrix}

$\begin{aligned} 324_5 & =\left(3 \times 5^2\right)+\left(2 \times 5^1\right)+\left(4 \times 5^0\right) \\ & =75+10+4 \\ & =89 \end{aligned}$

\begin{matrix} 124_{5} & = (1 \times 5^{2}) + (2 \times 5^{1}) + (4 \times 5^{0}) = 25 + 10 + 4 = 39 \end{matrix}

$\begin{aligned} 124_5 & =\left(1 \times 5^2\right)+\left(2 \times 5^1\right)+\left(4 \times 5^0\right) \\ & =25+10+4 \\ & =39 \end{aligned}$

\begin{matrix} 241_{5} & = (2 \times 5^{2}) + (4 \times 5^{1}) + (1 \times 5^{0}) = 50 + 20 + 1 = 71 \end{matrix}

$\begin{aligned} 241_5 & =\left(2 \times 5^2\right)+\left(4 \times 5^1\right)+\left(1 \times 5^0\right) \\ & =50+20+1 \\ & =71 \end{aligned}$

\begin{matrix} 231_{5} & = (2 \times 5^{2}) + (3 \times 5^{1}) + (1 \times 5^{0}) = 50 + 15 + 1 = 66 \end{matrix}

$\begin{aligned} 231_5 & =\left(2 \times 5^2\right)+\left(3 \times 5^1\right)+\left(1 \times 5^0\right) \\ & =50+15+1 \\ & =66 \end{aligned}$

Susun nombor mengikut urutan menaik = 124_{5}, 231_{5}, 241_{5}, 324_{5}

$\text { Susun nombor mengikut urutan menaik }=124_5, 231_5, 241_5, 324_5$

Praktis Kendiri 2.1a (Soalan 8 & 9) – Buku Teks Matematik Tingkatan 4 Bab 2 (Asas Nombor)

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