Question

The value of 0.18 (with the 1 and 8 repeating) is equal to:

• A. 2/11
• B. 2/33
• C. 2/99
• D. 8/33

Hint:

When two digits repeat, multiply by 100. When one digit repeats, as in 0.333..., multiply by 10. This helps eliminate the repeating part when you subtract.

Answer 1

The Correct Option is A

Let x = 0.181818... Since both the 1 and 8 repeat, we multiply by 100: 100x = 18.181818... Subtract the original equation from this new equation: 100x - x = 18.181818... - 0.181818... 99x = 18 x = 18/99 Simplify the fraction by dividing both numerator and denominator by their greatest common divisor (which is 9): x = (18 ÷ 9) / (99 ÷ 9) x = 2/11 Therefore, the correct answer is (A) 2/11.
Conclusion: The repeating decimal 0.181818... is equal to the fraction 2/11.