Which is the decimal expansion of ( \frac{17}{22} )?

Correct answer: (0.772727\ldots)

The direct answer is option A, 0.772727… . To convert 17/22 into a decimal, divide 17 by 22. Since 22 does not go into 17, write 0 and use 170; 22 goes 7 times, giving 154 and remainder 16. Bring down 0 to get 160; 22 goes 7 times, giving 154 and remainder 6. Bring down 0 to get 60; 22 goes 2 times, giving 44 and remainder 16. The remainder 16 has appeared before, so the digits 27 repeat: 17/22=0.772727… . Option A matches this. Option B, 0.727272…, is 8/11 and lacks the first 7. Option C, 0.818181…, equals 9/11, not 17/22. Option D does not correctly show the repeating pattern. Remember: when a remainder repeats in long division, the quotient digits from that point also repeat.