Looking for accurate SEBA Class 9 Maths Exercise 1.3 (Number Systems) textual solutions for the 2026–27 academic year? Access complete step-by-step solutions covering real numbers and their decimal expansions (terminating, non-terminating recurring), expressing repeating decimals(0.666…, 0.4777…, 0.001001…) in p/q form, finding non-terminating non-repeating irrational numbers between fractions, and predicting long division remainders to score top marks in your annual exams.
EXERCISE 1.3
1. Write the following in decimal form and say what kind of decimal expansion each has :
(i) 36/100
(i) 36/100
= 0.36
Decimal expansion: Terminating
(ii) 1/11
= 0.090909…
Decimal expansion: Non-terminating recurring
(iii) 4 1/8
= 33/8
= 4.125
Decimal expansion: Terminating
(iv) 3/13
= 0.230769230769…
Decimal expansion: Non-terminating recurring
(v) 2/11
= 0.181818…
Decimal expansion: Non-terminating recurring
(vi) 329/400
= 0.8225
Decimal expansion: Terminating
2. You know that 1/7 = 0.142857142857… Can you predict what the decimal expansions of 2/7, 3/7, 4/7, 5/7, 6/7 are, without actually doing the long division? If so, how?
[Hint : Study the remainders while finding the value of 1/7 carefully.]
Solution:
Yes, we can predict the decimal expansions by multiplying 1/7 by 2, 3, 4, 5, and 6.
2/7 = 2 × (1/7) = 2 × 0.142857142857… = 0.285714285714…
3/7 = 3 × (1/7) = 3 × 0.142857142857… = 0.428571428571…
4/7 = 4 × (1/7) = 4 × 0.142857142857… = 0.571428571428…
5/7 = 5 × (1/7) = 5 × 0.142857142857… = 0.714285714285…
6/7 = 6 × (1/7) = 6 × 0.142857142857… = 0.857142857142…
SEBA Class 9 Maths Exercise 1.3 Solutions
3. Express the following in the form p/q, where p and q are integers and q ≠ 0.
(i) 0.666…
Let x = 0.666… — (1)
Multiplying by 10 on both sides,
10x = 6.666… — (2)
Subtracting (1) from (2):
10x – x = 6.666… – 0.666…
9x = 6
x = 6/9
x = 2/3
Answer: 2/3
(ii) 0.4777…
Let x = 0.4777… — (1)
Multiplying by 10 on both sides,
10x = 4.777… — (2)
Multiplying by 100 on both sides,
100x = 47.777… — (3)
Subtracting (2) from (3):
100x – 10x = 47.777… – 4.777…
90x = 43
x = 43/90
Answer: 43/90
(iii) 0.001001…
Let x = 0.001001… — (1)
Multiplying by 1000 on both sides,
1000x = 1.001001… — (2)
Subtracting (1) from (2):
1000x – x = 1.001001… – 0.001001…
999x = 1
x = 1/999
Answer: 1/999
(iv) 0.5454…
Let x = 0.5454… — (1)
Multiplying by 100 on both sides,
100x = 54.5454… — (2)
Subtracting (1) from (2):
100x – x = 54.5454… – 0.5454…
99x = 54
x = 54/99
x = 6/11
Answer: 6/11
(v) 0.5959…
Let x = 0.5959… — (1)
Multiplying by 100 on both sides,
100x = 59.5959… — (2)
Subtracting (1) from (2):
100x – x = 59.5959… – 0.5959…
99x = 59
x = 59/99
Answer: 59/99
(vi) 0.345345…
Let x = 0.345345… — (1)
Multiplying by 1000 on both sides,
1000x = 345.345345… — (2)
Subtracting (1) from (2):
1000x – x = 345.345345… – 0.345345…
999x = 345
x = 345/999
x = 115/333
Answer: 115/333
(vii) 32.123535…
Let x = 32.123535… — (1)
Multiplying by 100 on both sides,
100x = 3212.3535… — (2)
Multiplying by 10000 on both sides,
10000x = 321235.3535… — (3)
Subtracting (2) from (3):
10000x – 100x = 321235.3535… – 3212.3535…
9900x = 318023
x = 318023/9900
Answer: 318023/9900
(viii) 0.3737…
Let x = 0.3737… — (1)
Multiplying by 100 on both sides,
100x = 37.3737… — (2)
Subtracting (1) from (2):
100x – x = 37.3737… – 0.3737…
99x = 37
x = 37/99
Answer: 37/99
Class 9 Maths Chapter 1 Exercise 1.3 Question Answer SEBA 2026-27
4. Express 0.99999… in the form p/q. Are you surprised by your answer? With your teacher and classmates discuss why the answer makes sense.
Solution:
Let x = 0.99999… — (1)
Multiplying by 10 on both sides,
10x = 9.99999… — (2)
Subtracting (1) from (2):
10x – x = 9.99999… – 0.99999…
9x = 9
x = 9/9
x = 1
Answer: 1
The difference between 1 and 0.99999… is infinitely small, so 0.99999… is equal to 1.
5. What can the maximum number of digits be in the repeating block of digits in the decimal expansion of 1/17? Perform the division to check your answer.
Solution:
The maximum number of digits in the repeating block of digits for 1/17 is (17 – 1) = 16 digits.
By long division:
1/17 = 0.05882352941176470588235294117647…
There are 16 digits in the repeating block.
Decimal Expansions Class 9 SEBA Ex 1.3 Solutions
6. Look at several examples of rational numbers in the form p/q (q ≠ 0), where p and q are integers with no common factors other than 1 and having terminating decimal representations (expansions). Can you guess what property q must satisfy?
Solution:
The prime factorisation of q must have only powers of 2, powers of 5, or both.
Property: q = (2ᵐ) × (5ⁿ), where m and n are non-negative integers.
7. Write three numbers whose decimal expansions are non-terminating non-recurring.
Solution:
Three non-terminating non-recurring numbers are:
(i) 0.01001000100001…
(ii) 0.202002000200002…
(iii) 0.505005000500005…
SEBA Class 9 Maths Chapter 1 Exercise 1.3 Textbook Answers
8. Find three different irrational numbers between the rational numbers 5/7 and 9/11.
Solution:
5/7 = 0.714285…
9/11 = 0.818181…
Three irrational numbers between 0.714285… and 0.818181… are:
(i) 0.73073007300073…
(ii) 0.75075007500075…
(iii) 0.79079007900079…
9. Classify the following numbers as rational or irrational :
(i) √(23)
(ii) √(225)
(iii) 0.3796
(iv) 7.478478…
(v) 1.101001000100001…
(i) √(23)
Answer: Irrational (23 is not a perfect square)
(ii) √(225)
= 15
Answer: Rational
(iii) 0.3796
Answer: Rational (terminating decimal)
(iv) 7.478478…
Answer: Rational (non-terminating recurring decimal)
(v) 1.101001000100001…
Answer: Irrational (non-terminating non-recurring decimal)
10. Assertion (A) : 0.666… and 0.37777… are rational numbers.
Reason (R) : If the decimal expansion of a real number is either terminating or non terminating recurring it is a rational number.
(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
(C) Assertion (A) is true, Reason (R) is false.
(D) Assertion (A) is false, Reason (R) is true.
Option (A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
Express Repeating Decimals in p/q Form Class 9 SEBA
📐 Updated Solutions Notice: This page features complete, step-by-step SEBA Class 9 Mathematics Chapter 1 (Number Systems) Exercise 1.3 Textual Solutions updated for the 2026–27 academic session. All real number decimal expansions, algebraic $p/q$ conversions for non-terminating repeating decimals, and quotient prediction steps strictly follow the latest revised Assam Board (SEBA) curriculum.
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