source: ncert_exercises
topic: numbers
class_level: class_9
chapter: ch1
exercise: ex1.3
difficulty: intermediate
Class 9 | Ch1: Number Systems | Exercise 1.3
Q1. Write in decimal form and state type: (i) 36/100 (ii) 1/11 (iii) 4⅛ (iv) 3/13 (v) 2/11 (vi) 329/400 Answer: (i) 0.36 Terminating. (ii) 0.0̄9̄ Non-terminating recurring. (iii) 4.125 Terminating. (iv) 0.230769̄ Non-terminating recurring. (v) 0.1̄8̄ Non-terminating recurring. (vi) 0.8225 Terminating. ✅
Q2. Predict 2/7, 3/7, 4/7, 5/7, 6/7 using 1/7 = 0.142857̄. Answer: 2/7=0.285714̄, 3/7=0.428571̄, 4/7=0.571428̄, 5/7=0.714285̄, 6/7=0.857142̄. ✅ All cyclic permutations of 142857.
Q3. Express in p/q form: (i) 0.6̄ (ii) 0.47̄ (iii) 0.001̄ Answer: (i) x=0.666... → 9x=6 → x=2/3. (ii) x=0.4747... → 99x=47 → x=47/99. (iii) x=0.001001... → 999x=1 → x=1/999. ✅
Q4. Express 0.9999... in p/q form. Answer: x=0.999... → 10x=9.999... → 9x=9 → x=1. ✅ 0.9999...=1. No number exists between them — they are equal.
Q5. Maximum digits in repeating block of 1/17? Answer: Max = n-1 = 16 for 1/17. Actual: 1/17 = 0.0588235294117647̄ — repeating block has exactly 16 digits. ✅
Q6. What property must q have for p/q to terminate? Answer: q must have ONLY 2 and 5 as prime factors. q = 2^m × 5^n. Example: 1/8=1/2³ terminates. 1/6=1/(2×3) does NOT (factor 3). ✅
Q7. Write three non-terminating non-recurring decimals. Answer: √2=1.41421..., √3=1.73205..., π=3.14159... ✅ Any irrational works.
Q8. Find three irrationals between 5/7 and 9/11. Answer: 5/7=0.7142... and 9/11=0.8181... Three irrationals: 0.72020020002..., 0.75075007500..., 0.80800800080... ✅
Q9. Classify as rational or irrational: (i)√23 (ii)√225 (iii)0.3796 (iv)7.478478... (v)1.101001000100001... Answer: (i)Irrational (ii)Rational—√225=15 (iii)Rational—terminating (iv)Rational—recurring (v)Irrational—non-terminating non-recurring. ✅