Here you will find CBSE NCERT Solutions for Class 10 Maths Chapter 1 Exercise 1.4 PDF through which you can complete you hometask on time. These NCERT Solutions for Class 10 Maths can be used to solve difficult problems in the examinations.
Book Name | Class 10 Mathematics NCERT Textbook |
Chapter | Chapter 1 Real Numbers |
Exercise | Ex 1.4 |
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:
(i) 13/ 3125
(ii) 17/18
(iii) 64/455
(iv) 15/1600
(v) 29/343
(vi) 23/2^{3}5^{3 }
(vii) 129/2^{2}5^{7}7^{5 }
(viii) 16/15
(ix) 35/50
(x) 77/ 210
Solution
(i) 13/3125
∵ 3125 = 5 × 5 × 5 × 5 × 5 = 5^{5}
= 2^{0} × 5^{5}, |∵ 2^{0} = 1
which is of the form (2^{n} · 5^{m})
∴ 13/3125 is a terminating decimal.
i.e., 13/3125 will have a terminating decimal expansion.
(ii) 17/8
∵ 8 = 2 × 2 × 2 = 2^{3} = 1 × 2^{3}
= 5^{0} × 2^{3}, which is of the form 5^{m} · 2^{n}
∴ 17/8 will have a terminating decimal expansion.
(iii) 64/455
∵ 455 = 5 × 7 × 13, which is not of the form 2^{n} · 5^{m}
∴ 64/455 will have a non-terminating repeating decimal expansion.
(iv) 15/1600
∵ 1600 = 2 × 2 × 2 × 2 × 2 × 2 × 5 × 5
= 2^{6} × 5^{2}, which is of the form 2^{n} · 5^{m}
∴ 15/1600 will have a terminating decimal expansion.
(v) 29/343
∵ 343 = 7 × 7 × 7 = 73, which is not of the form 2^{n} · 5^{m}.
∴ 29/343 will have a non-terminating repeating decimal expansion.
(vi) 23/2^{3}5^{2}
Let p/q = 23/2^{3}5^{2}
i.e., q = 2^{3} · 5^{2}, which is of the form 2n · 5m.
∴ 23/2^{3}5^{2 }will have a terminating decimal expansion.
(vii) 129/2^{2}5^{7}7^{5 }
Let p/q = 129/2^{2}5^{7}7^{5 }
i.e., q = 2^{2} · 5^{7} · 7^{5}, which is not of the form 2^{n} · 5^{m}.
∴ 129/2^{2}5^{7}7^{5 }will have a non-terminating repeating decimal expansion.
(viii) 6/15
∴ 6/15 will have a terminating decimal expansion.
(ix) 35/50
∵ 50 = 2 × 5 × 5 = 21 × 52, which is of the form 2n · 5m.
∴ 35/50 will have a terminating decimal expansion.
(x) 77/210
∵ 210 = 2 × 3 × 5 × 7 = 21 · 31 · 51 · 71,
which is not of the form of 2n · 5m.
∴ 77/ 210 will have a non-terminating repeating decimal expansion.
2. Write down the decimal expansions of those rational numbers in Question 1 above which have terminating decimal expansions.
(i) 13/ 3125
(ii) 17/18
(iii) 64/455
(iv) 15/1600
(v) 29/343
(viii) 6/15
(ix) 35/50
(x) 77/ 210
Solution
(i) 13/3125
(ii) 17/18
(iii) 64/455 represents non-terminating repeating decimal expansion.
(iv) 15/1600
(v) 29/343, represents a non-terminating repeating decimal expansion.
(viii) 6/15
6/15 = 2/5
= 2/5×2/2
= 4/10 = 0.4
(ix) 35/50
35/50 = 0.7
(x) 77/ 210, represents a non-terminating repeating decimal expansion.
Given Class 10 Maths Chapter 1 Real numbers NCERT Solutions can be used to score good marks in the examinations and prepare your own answers.