Chapter 1: Number Systems

Q1. Is 0.9999... equal to 1? Prove it.

Solution

Let x = 0.9999...
10x = 9.9999...
10x - x = 9
9x = 9, x = 1
Therefore 0.9999... = 1

Q2. Simplify: (√5 + √2)/(√5 - √2).

Solution

Multiply by conjugate:
= (√5 + √2)²/((√5)² - (√2)²)
= (5 + 2 + 2√10)/(5 - 2)
= (7 + 2√10)/3