# 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

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.

2. Integer numbers set is denoted by which letter?
a) N
b) W
c) Q
d) Z

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…}

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

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

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”.

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

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

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.

8. How many whole numbers are there between -3 and 3 (Including -3 and 3)?
a) Four
b) Zero
c) Seven
d) Three

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

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.

10. Rational numbers are denoted by ______
a) N
b) Z
c) Q
d) W

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

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