Question

1. which decimal is the equivalent of \\(\frac{2}{9}\\)? a. 0.52 b. 0.5622 c. \\(0.overline{9}\\) d. 0.22222

Explanation:

Step1: Divide 2 by 9

To find the decimal equivalent of $\frac{2}{9}$, we perform the division: $2 \div 9$.
When we divide 2 by 9, we get $0.22222\ldots$ (the digit 2 repeats infinitely).

Step2: Compare with options

We compare the result of $2 \div 9$ with the given options:

• Option A: $0.52$ is not equal to $0.222\ldots$
• Option B: $0.5622$ is not equal to $0.222\ldots$
• Option C: $0.\overline{9}$ is equal to 1, not $0.222\ldots$
• Option D: $0.22222$ (a finite decimal approximation of the repeating decimal $0.\overline{2}$) matches the result of $2 \div 9$.

Answer:

D. 0.22222