NUMBER BASE SYSTEM

CONTENT

1. Conversion from other bases to base 10 and vice versa.
2. 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.