Class 10 Maths Chapter 1 Exercise 1.4 Solutions – Real Numbers | Assam Eduverse

Welcome to Assam Eduverse, your trusted learning partner. In this post, we bring you step-by-step NCERT solutions for Class 10 Maths Chapter 1 – Real Numbers (Exercise 1.4) based on the latest NCERT and SEBA curriculum.

📘 Chapter 1: Real Numbers

🧮 Exercise 1.4 – NCERT Solutions

✅ Question 1:

Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion. Give reasons.

(i) 13/3125
(ii) 17/8
(iii) 64/455
(iv) 15/1600
(v) 29/343
(vi) 23/2³ × 5²
(vii) 129/2² × 3⁷ × 5²
(viii) 6/15

Answer:

To check whether a rational number has a terminating decimal, factorize the denominator.
If the denominator (after simplifying) has only 2 and/or 5 as prime factors, it’s terminating.
Otherwise, it’s non-terminating repeating.

• (i) 13/3125
  → 3125 = 5⁵ ⇒ Only 5 → ✅ Terminating

• (ii) 17/8
  → 8 = 2³ ⇒ Only 2 → ✅ Terminating

• (iii) 64/455
  → 455 = 5 × 7 × 13 ⇒ 7 & 13 are not allowed → ❌ Non-terminating repeating

• (iv) 15/1600
  → 1600 = 2⁶ × 5² ⇒ Only 2 & 5 → ✅ Terminating

• (v) 29/343
  → 343 = 7³ ⇒ 7 is not allowed → ❌ Non-terminating repeating

• (vi) 23/(2³ × 5²)
  → Only 2 & 5 → ✅ Terminating

• (vii) 129/(2² × 3⁷ × 5²)
  → Contains 3 ⇒ ❌ Non-terminating repeating

• (viii) 6/15
  → 15 = 3 × 5 ⇒ 3 is not allowed → ❌ Non-terminating repeating

✅ Question 2:

Write down the decimal expansions of the following rational numbers and state the nature of each.

(i) 1/3
(ii) 4/7
(iii) 1/8
(iv) 3/11
(v) 329/400

Answer:

• (i) 1/3 = 0.333… → Non-terminating repeating

• (ii) 4/7 = 0.571428571428… → Non-terminating repeating

• (iii) 1/8 = 0.125 → Terminating

• (iv) 3/11 = 0.272727… → Non-terminating repeating

• (v) 329/400 = 0.8225 → Terminating