Page 24 - Hybrid PBD 2022 Tg 4 - Matematik

Matematik Tingkatan 4 Bab 2 Asas Nombor
7. Tukarkan setiap nombor berikut kepada nombor dalam asas yang dinyatakan dalam kurungan.
Convert each of the following numbers to a number in base stated in the brackets. SP 2.1.2 TP3

(a) 231 4 (Asas enam / Base six)
57 8 (Asas tiga / Base three)

231 4 = (2 × 4 ) + (3 × 4 ) + (1 × 4 )
1
0
2
0
1
57 8 = (5 × 8 ) + (7 × 8 ) = 32 + 12 + 1
= 40 + 7
= 47 10 = 45 10
6 4 5 Baki / Remainder
3 4 7 Baki / Remainder 6 7 – 3
3 1 5 – 2 6 1 – 1
3 5 – 0 0 – 1
3 1 – 2
0 – 1 Maka / Thus, 231 4 = 113 6

Maka / Thus, 57 8 = 1202 3

(b) 324 5 (Asas sembilan / Base nine) (c) 111011 2 (Asas tujuh / Base seven)

0
1
2
3
4
5
324 5 = (3 × 5 ) + (2 × 5 ) + (4 × 5 ) 111011 2 = (1 × 2 ) + (1 × 2 ) + (1 × 2 )
= 75 + 10 + 4 + (0 × 2 ) + (1 × 2 ) + (1 × 2 )
2
1
0
= 89 10 = 32 + 16 + 8 + 0 + 2 + 1
= 59 10
9 8 9 Baki / Remainder
9 9 – 8 7 5 9 Baki / Remainder
9 1 – 0 7 8 – 3
1 – 1
7
0 – 1
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0 – 1
Maka / Thus, 324 5 = 108 9
Maka / Thus, 111011 2 = 113 7
8. Tukarkan setiap nombor berikut kepada nombor dalam asas lapan. SP 2.1.2 TP3
Convert each of the following numbers to a number in base eight.

101111 2

Kaedah / Method 1

1 0 1 1 1 1
Number Tip Penting
Nilai tempat 2 1 0 2 1 0 1. Asingkan digit dalam kumpulan tiga digit,
Place value 2 2 2 2 2 2 bermula dari kanan ke kiri.
Nilai digit Split digits in group of three, from right to left.
Digit value 4 0 1 4 2 1 2. Tambahkan nilai digit bagi setiap kumpulan.
Add up the digit values of each group.
Asas 8 4 + 0 + 1 4 + 2 + 1 3. Gabungkan nombor dalam asas lapan.
Base 8 = 5 = 7 Combine the number in base eight.

101111 2 = 57 8

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