Page 10 - Spotlight A+ Form 4 & 5 Mathematics KSSM

Form
4
Chapter 2 Number Bases Mathematics
Convert numbers from one base to another Solution:
using various methods (a) 57 = 32 + 16 + 8 + 1
10 = 2 + 2 + 2 + 2 0
5
4
3
1. The conversion of numbers from one base = 1 × 2 + 1 × 2 + 1 × 2 + 0 × 2
3
4
2
5
to base ten can be carried out by using place + 0 × 2 + 1 x 2 0
1
values. = 111001 CHAP.
2 2
Example 7 Place value 2 5 2 4 2 3 2 2 2 1 2 0
Digit 1 1 1 0 0 1
Convert each of the following numbers to a
number in base ten. (b) 2 57 Remainder
(a) 11010 (b) 123 4 2 28 … 1
2
(c) 4031 (d) 652
5 8 2 14 … 0
Solution:
2 7 … 0
(a) Place value 2 4 2 3 2 2 2 1 2 0 2 3 … 1
2 1 … 1
Digit 1 1 0 1 0
0 … 1
11010
2 57 = 111001
3
4
= 1 × 2 + 1 × 2 + 0 × 2 + 1 × 2 + 0 × 2 0 10 2
2
1
= 16 + 8 + 0 + 2 + 0 Calculator
= 26
10
Press:  MODE MODE 3 DEC
(b) Place value 4 2 4 1 4 0
2 5 7 = BIN
Digit 1 2 3
1
2
123 = 1 × 4 + 2 × 4 + 3 × 4 0 Try question 8 in Formative Zone 2.1
4
= 16 + 8 + 3
= 27 Example 9
10
By using place values, convert 65 to a number in
(c) ©PAN ASIA PUBLICATIONS
5
5
5
5
0
2
1
3
Place value
10
(a) base five, (b) base eight, (c) base three.
Digit 4 0 3 1
Solution:
4031 = 4 × 5 + 0 × 5 + 3 × 5 + 1 × 5 0 (a) 65 = 50 + 15
2
3
1
5
= 500 + 0 + 15 + 1 10 = 2 × 25 + 3 × 5
= 516 2 1 0
10 = 2 × 5 + 3 × 5 + 0 × 5
= 230
(d) Place value 8 2 8 1 8 0 5
Place value 5 2 5 1 5 0
Digit 6 5 2
Digit 2 3 0
1
2
652 = 6 × 8 + 5 × 8 + 2 × 8 0 (b) 65 = 64 + 1
8
= 384 + 40 + 2 10 = 8 + 1
2
= 426
2
1
10 = 1 × 8 + 0 × 8 + 1 × 8 0
= 101
Try question 7 in Formative Zone 2.1 8
Place value 8 2 8 1 8 0
2. The conversion of numbers in base ten to a Digit 1 0 1
number in another base can be carried out by (c) 65 = 54 + 9 + 2
10
using place values and division. = 2 × 27 + 9 + 2
1
2
= 2 × 3 + 1 × 3 + 0 × 3 + 2 × 3 0
3
Example 8 = 2102 3
Place value 3 3 3 2 3 1 3 0
Convert 57 to a number in base two by using
10 2 1 0 2
(a) place values, (b) division. Digit
Try question 9 in Formative Zone 2.1
2.1.2 23
02 Spotlight A+ MM F4.indd 23 19/01/2021 9:29 AM