5
NUMBER SYSTEMS
EXERCISE 1.1
1.
Is zero a rational number? Can you write it in the form P, where p and q are integers
9
and q +02
Find six rational numbers between 3 and 4.
2.
3 4
3. Find five rational numbers between and
5 51
4. State whether the following statements are true or false. Give reasons for your answer
(1) Every natural number is a whole number.
(ii) Every integer is a whole number. F
Answers
Answer:
Number System
Question 1: Is zero a rational number? Can you write it in the form of p/q, where p and q are integers and q ≠ 0?
Answer: We know that, raional number is a number which can be written in the form of p/q, where q is not equal to zero. Thus,
(a) Yes, zero is a rational number, as it can be written in the form of p/q.
(b) Since, 0 (zero) is an integer thus, zero can be written in the form of p/q. Example : 0/1, 0/2, 0/3, etc. where 0 (zero) is an integer.9 Mathexcellup logo
Number System
Exercise 1.1 Part 1
Number System
Question 1: Is zero a rational number? Can you write it in the form of p/q, where p and q are integers and q ≠ 0?
Answer: We know that, raional number is a number which can be written in the form of p/q, where q is not equal to zero. Thus,
(a) Yes, zero is a rational number, as it can be written in the form of p/q.
(b) Since, 0 (zero) is an integer thus, zero can be written in the form of p/q. Example : 0/1, 0/2, 0/3, etc. where 0 (zero) is an integer.
Question 2: Find six rational numbers between 3 and 4.
Answer:First method to find rational number between two number:
A rational number between two numbers can be found by calculating average of two given numbers.Thus, six rational numbers between given two numbers i.e. 3 and 4 can be calculated as follows:
(1) First rational number between 3 and 4 can be calculated by finding average between them.
3
+
4
2
=
7
2
(2) As 7/2 is a rational number between 3 and 4, consequently, rational number between 3 and 7/2 will be one of the rational number between 3 and 4, which can be found by calcuating average between 3 and 7/2
(
7
2
)
+
3
2
=
7
+
6
2
2
=
13
2
2
=
13
2
×
2
=
13
4
(3) Again as as 7/2 is a rational number between 3 and 4, consequently, rational number between 4 and 7/2 will be the rational number between 3 and 4, which can be found by average between 4 and 7/2
4
+
(
7
2
)
2
=
8
+
7
2
2
=
15
2
2
=
15
2
×
2
=
15
4
(4) Similarly, rational number between 3 and 13/4 will be the rational number between 3 and 4, since 13/4 is a rational number between 3 and 4. Thus next rational number between 3 and 4 can be found by calculating average between 3 and 13/4
3
+
13
4
2
=
12
+
13
4
2
=
25
4
2
=
25
4
×
2
=
25
8
Answer:
- no 0 is not a rational number, yeah we can write it in form p
- 3.2, 3.5, 3.4, 3.3, 3.6, 3.8
- 5.6, 9.6, 8.3, 10.6, 29.8
- 1. true 2. false