Question

Prove algebraically that the recurring decimal \(0.72222\) is equal to \( \frac{8}{11} \).

A) 1/11
B) 2/11
C) 4/11
D) 8/11

Answer 1

By setting the recurring decimal 0.72222... equal to x and multiplying by 10, then subtracting the original value of x, we get 9x = 6.5, which simplifies to x = 8/11, proving that the recurring decimal is indeed equal to 8/11.

Step-by-step explanation:

To prove algebraically that the recurring decimal 0.72222... is equal to ⅔, we first represent the recurring decimal as an algebraic expression. Let x equal to 0.72222... Multiplying both sides of the equation by 10, we have 10x equal to 7.2222.... Now, by subtracting the original equation from this new equation, we eliminate the recurring part:

10x = 7.2222...
x = 0.72222...

Subtracting these equations gives us:

9x = 6.5

Solving for x gives us x equals ⅔. Therefore, 0.72222... is algebraically proven to be equal to ⅔.