Chapter 1. Number Systems NIOS Class 10 Mathematics Chapter-Wise Important Questions and Answers
Chapter 1. Number Systems | NIOS Class 10 Mathematics Important Questions, Fully Solved Answers, and Chapter-wise Exam Preparation Guide.
Chapter 1 . Number Systems
Optional Questions and Answers for Number Systems [1 Mark]
Question: Which of the following is not an integer?
(a) 
(b) 2.35 (c) 
(d) – 1
Answer: (d) – 1
Question: Which of the following is a whole number ?
(a) 15 (b) – 6 (c) 0.25 (d) 
Answer: (a) 15
Question: The lowest form of the rational number 
is
(a) 
(b) 
(c) 
(d) 
Answer: (b)
[ We have, 
]
Question: The equivalent forms of the rational number 
is
(a) 
(b) 
(c) 
(d) 
Answer: (c)
[ We have, 
]
Question: 
is equal to
(a) 
(b) 
(c) 
(d) 
Answer: (d) 
[ We have, 
]
Question: The product of 
is
(a) 12 (b) – 6 (b) 6 (d) 24
Answer: (b) – 6
[ We have, 
]
Question: The rational numbers between 0.27 and 0.28 is
(a) 0.275 (b) 0.29 (c) 0.26 (d) 0.32
Answer: (a) 0.275
[We have, 
]
Question: Decimal representation of a rational number cannot be :
(a) terminating (b) non-terminating
(c) non-terminating repeating (d) non-terminating and non-repeating
Answer: (d) non-terminating and non-repeating .
Question: The value of 0.3333333……. in the form 
, where 
and 
are integers and 
, is :
(a) 
(b) 
(c) 1 (d) 
Answer: (d) 
[ Let 
] .
Question: Between two rational numbers :
(a) there is no rational number
(b) there is exactly one rational number
(c) there are infinitely many rational numbers
(d) There are only rational numbers and no irrational numbers
Answer: (c) there are infinitely many rational numbers .
Question: Every rational number is :
(a) a natural number (b) an integer (c) a real number (d) a whole number
Answer: (C) a real number
Short Questions and Answers for Number Systems [1 or 2 Mark]
Question: Identify natural numbers, whole numbers and integers from the following:-
15, 22, – 6, 7, – 13, 0, 12, – 12, 13, – 31
Solution: Natural numbers are: 7, 12, 13, 15 and 22
Whole numbers are: 0, 7, 12, 13, 15 and 22
Integers are: – 31, – 13, – 12, – 6, 0, 7, 12, 13, 15 and 22
Question: From the following, identify those which are (i) not natural numbers (ii) not whole numbers
– 17, 15, 23, – 6, – 4, 0, 16, 18, 22, 31
Solution: (i) – 17, – 6, – 4 and 0 are not natural numbers.
(ii) – 17, – 6, – 4 are not whole numbers.
Question: Write the following rational numbers in their lowest terms:
(a) 
(b) 
(c) 
Solution: (a) 
is the lowest form of the rational number 
(b) 
∴ 
is the lowest form of the rational number 
.
(c) 
∴ 
is the lowest form of the rational number 
.
Question: Write five equivalent forms of the following rational numbers: (a) 
(b) 
Solution: (a) 
∴ Five equivalent forms of 
are 
(b) 
∴ Five equivalent forms of 
are 
Question: Add the following rational numbers:
(a) 
(b) 
(c) 
Solution: (a) 
(b) 
(c) 
Question: Add each of the following rational numbers:
(a) 
(b) 
(c) 
Solution: (a) 
(b) 
(c) 
Question: Multiply the following rational numbers:
(a) 
(b) 
(c) 
Solution: (a) 
(b) 
(c) 
Question: Simply the following:
(a) 
(b) 
(c) 
Solution: (a) 
(b) 
(c) 
Long Questions and Answers for Number Systems [ 3 or 4 Mark]
Question: Express (i) 0.666........ (ii) 0.374374........... in 
form .
Solution: (i) Let, 
(ii) 0.374374............
Let, 
Question: Express 
in the form , where p and q are integers and q ≠ 0 .
Solution: Let, 
Question: Express 
in the form , where p and q are integers and q ≠ 0 .
Solution: Let , 
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