Question

Part A: Using complete sentences, explain how to convert zero point 22 repeating to a fraction. (2 points)

Part B: Is zero point 22 repeating times square root of 112 end square root rational or irrational? Justify your answer. (2 points)

Answer 1

Answer:

a) $\frac{2}{9}$

b) Irrational

Step-by-step explanation:

a) Let $y=0.\bar2.....(a)$

Then $100y=22.\bar2.....(b)$

Subtract (a) from (b)

$100y-y=22.\bar2-0.\bar2$

$\implies 99y=22$

$y=\frac{22}{99}=\frac{2}{9}$

b) From part a) $0.\bar2$ is a rational number but $\sqrt{112}=4\sqrt{7}$ is an irrational number.

But $0.\bar2\times \sqrt{112}$ is not a rational number because the product of a rational number and an irrational number is an irrational number.