NUMBER BASE SYSTEM
CONTENT
- Conversion from other bases to base 10 and vice versa.
- Conversion of decimal fraction in other bases to base 10 and vice versa.
Concept of expanded notation: Every decimal number X can be expressed uniquely in the form:
This is known as the expanded notation.
EXAMPLE 1: Express the following in expanded notation form.
(a) 45078 (b) 0235 (c) 930.133
Solution:
EXAMPLE 2: Write the following in expanded notation form.
(a) 32.516
(b) 0.10012
Solution:
CLASS ACTIVITY
1. Write the following decimal numbers in an expanded notation form
(a) 402
(b) 60.008
(c) 0.0153
2. Write the following numbers in their ordinary form
(a) 60 × 103 + 0 × 102 + 5 × 101 + 8 × 100
(b) 4 × 101 + 3 × 100 + 0 × 10−1 + 2 × 10−2
(c) 5 × 70 + 8 × 7−1 + 9 × 7−2
THE CONCEPT OF NUMBER BASE SYSTEM
A number system is defined by the base it uses, the base being the number of different symbols required by the system to represent any of the infinite series of numbers.
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