Mathematics Questions and Answers – Number Systems Basics

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This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Number Systems Basics”.

1. Which of the following is Natural number?
a) 3.5
b) 7
c) 0
d) -2
View Answer

Answer: b
Explanation: Natural numbers contains {1, 2, 3…}.
3.5 is not an integer, so it is not natural number.
0 and -2 are not natural numbers because they are not the part of natural numbers’ set.
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2. Integer numbers set is denoted by which letter?
a) N
b) W
c) Q
d) Z
View Answer

Answer: d
Explanation: Integers are denoted by Z where Z contains {…-2, -1, 0, 1, 2 …}.

3. Find the incorrect option (Assume conventional notations).
a) Q = p/q where p and q are integers and q=0
b) N = {1, 2, 3…}
c) W = {0, 1, 2, 3…}
d) Z = {…-2, -1, 0, 1, 2…}
View Answer

Answer: a
Explanation: Q = p/q where p and q are integers and q = 0 is an incorrect option. In the option, q=0 is given which is incorrect it should be q ≠ 0. All other options are correct since N set includes all positive integers, W set includes all integers and zero and Z set includes zero and all positive and negative integers.
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4. Zero is a rational number.
a) False
b) True
View Answer

Answer: b
Explanation: 0 = 0/1 = 0/2 =… and so on. Here 0 and any number in the denominator is integer and denominator ≠ 0 so according to definition, zero is a rational number.

5. There are _________ rational numbers between 2 and 3.
a) zero
b) two
c) infinite
d) data is insufficient
View Answer

Answer: c
Explanation: Between 2 and 3, there are infinite numbers which are rational numbers like 11/5, 12/5, 13/6, 17/8 and so on. They all are integers and no denominator is zero so they are rational numbers. Thus, we can find infinite numbers who satisfies this condition.
So we can say that “There are infinite rational numbers between any two integers”.
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6. Which of the following option is true based on the below statements?
i) All integers are rational numbers.
ii) All rational numbers are integers.
a) Both statements are true
b) Statement (i) is true and Statement (ii) is false
c) Statement (i) is false and Statement (ii) is true
d) Both statements are false
View Answer

Answer: b
Explanation: All integers {…-2, -1, 0, 1, 2…} can be represented in the form of p/q where p and q are integers and q ≠ 0. Example – 0/1, 2/1, etc. Hence, all integers are rational numbers.
2/5 is rational number but 2/5= 0.4 which is not an integer. Hence, all rational numbers are not integers.

7. Which of the following is not rational number?
a) 8/9
b) 5/7
c) -3/2
d) √2
View Answer

Answer: d
Explanation: A number is said to be rational number if it can be represented by p/q where p and q are integers and q≠0 but √2 = √2/1 and √2 = 1.414213… which is not integer hence, √2 is not rational number.
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8. How many whole numbers are there between -3 and 3 (Including -3 and 3)?
a) Four
b) Zero
c) Seven
d) Three
View Answer

Answer: a
Explanation: W = {0, 1, 2, 3…….}. So whole numbers between -3 and 3 are 0, 1, 2 and 3.
Hence, there are four numbers between -3 and 3 that are whole numbers.

9. N is subset of W, Z and Q. (Assume conventional notations)
a) True
b) False
View Answer

Answer: a
Explanation: N = {1, 2, 3….}
W = {0, 1, 2, 3….}
Z = {…-3, -2, -1, 0, 1, 2, 3….}
Q = p/q where p and q are integers and q ≠ 0
We can see that all the members of N are contained in W, Z and Q hence, it is true that N is subset of W, Z and Q.
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10. Rational numbers are denoted by ______
a) N
b) Z
c) Q
d) W
View Answer

Answer: c
Explanation: Rational numbers are denoted by Q. Q = p/q where p and q are integers and q ≠ 0.

Sanfoundry Global Education & Learning Series – Mathematics – Class 9.

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Manish Bhojasia - Founder & CTO at Sanfoundry
Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn | Youtube | Instagram | Facebook | Twitter