Question

A2. Find the rational number whose decimal expansion is 0.3344444...

Answer 1

301/900.

Explanation:

0.33 = 33/100

44.44444,, = 44/99

So 0.004444...

= 44/9900

33/100 + 44/9900

301/900

Answer 2

`\large\boxed{0.334444...=(301)/(900)}`

Explanation:

`x=0.334444...\qquad\text{multiply both sides by 100}\\\\100x=33.4444...\qquad\text{multiply both sides by 10}\\\\1000x=334.4444...\qquad\text{subtract}\ 100x\ \text{from}\ 1000x\\\\1000x-100x=334.4444...-33.4444...\\\\900x=301\qquad\text{divide both sides by 900}\\\\x=(301)/(900)`