UMBER SYSTEMS
EXERCISE 1.1
1. Is zero a rational number? Can you write it in the form 2. wher
and q +02
2. Find six rational numbers between 3 and 4.
3
. Find five rational numbers between and
5
State whether the following statements are true or false. Give re
(1) Every natural number is a whole number.
(ii) Every integer is a whole number.
(1) Every rational number is a whole
Answers
Answer:
Is zero a rational number? Can you write it in the form p/q where p and q are integers and q ≠ 0?
Solution:
We know that, a number is said to be rational if it can be written in the form p/q , where p and q are integers and q ≠ 0.
Taking the case of ‘0’,
Zero can be written in the form 0/1, 0/2, 0/3 … as well as , 0/1, 0/2, 0/3 ..
Since it satisfies the necessary condition, we can conclude that 0 can be written in the p/q form, where q can either be positive or negative number.
Hence, 0 is a rational number.
2. Find six rational numbers between 3 and 4.
Solution:
There are infinite rational numbers between 3 and 4.
As we have to find 6 rational numbers between 3 and 4, we will multiply both the numbers, 3 and 4, with 6+1 = 7 (or any number greater than 6)
i.e., 3 × (7/7) = 21/7
and, 4 × (7/7) = 27/7. The numbers in between 21/7 and 28/7 will be rational and will fall between 3 and 4.
Hence, 22/7, 23/7, 24/7, 25/7, 26/7, 27/7 are the 6 rational numbers between 3 and 4.
3. Find five rational numbers between 3/5 and 4/5.
Solution:
There are infinite rational numbers between 3/5 and 4/5.
To find out 5 rational numbers between 3/5 and 4/5, we will multiply both the numbers 3/5 and 4/5
with 5+1=6 (or any number greater than 5)
i.e., (3/5) × (6/6) = 18/30
and, (4/5) × (6/6) = 24/30
The numbers in between18/30 and 24/30 will be rational and will fall between 3/5 and 4/5.
Hence,19/30, 20/30, 21/30, 22/30, 23/30 are the 5 rational numbers between 3/5 and 4/5
4. State whether the following statements are true or false. Give reasons for your answers.
(i) Every natural number is a whole number.
Solution:
True
Natural numbers- Numbers starting from 1 to infinity (without fractions or decimals)
i.e., Natural numbers= 1,2,3,4…
Whole numbers- Numbers starting from 0 to infinity (without fractions or decimals)
i.e., Whole numbers= 0,1,2,3…
Or, we can say that whole numbers have all the elements of natural numbers and zero.
Every natural number is a whole number; however, every whole number is not a natural number.
(ii) Every integer is a whole number.
Solution:
False
Integers- Integers are set of numbers that contain positive, negative and 0; excluding fractional and decimal numbers.
i.e., integers= {…-4,-3,-2,-1,0,1,2,3,4…}
Whole numbers- Numbers starting from 0 to infinity (without fractions or decimals)
i.e., Whole numbers= 0,1,2,3….
Hence, we can say that integers include whole numbers as well as negative numbers.
Every whole number is an integer; however, every integer is not a whole number.
(iii) Every rational number is a whole number.
Solution:
False
Rational numbers- All numbers in the form p/q, where p and q are integers and q≠0.
i.e., Rational numbers = 0, 19/30 , 2, 9/-3, -12/7…
Whole numbers- Numbers starting from 0 to infinity (without fractions or decimals)
i.e., Whole numbers= 0,1,2,3….
Hence, we can say that integers includes whole numbers as well as negative numbers.
Every whole numbers are rational, however, every rational numbers are not whole numbers.
Answer:
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NCERT Solutions for Class 9 Maths Exercise 1.1
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NCERT solutions for Class 9 Maths Number Systems Download as PDF
NCERT Solutions for Class 9 Maths Exercise 1.1
NCERT Solutions for Class 9 Maths Number Systems
1. Is zero a rational number? Can you write it in the form, where p and q are integers and?
Ans. Consider the definition of a rational number.
A rational number is the one that can be written in the form of, where p and q are integers and.
Zero can be written as.
So, we arrive at the conclusion that 0 can be written in the form of, where q is any integer.
Therefore, zero is a rational number.
NCERT Solutions for Class 9 Maths Exercise 1.1
2. Find six rational numbers between 3 and 4.
Ans. We know that there are infinite rational numbers between any two numbers.
A rational number is the one that can be written in the form of, where p and q are
Integers and .
We know that the numbers all lie between 3 and 4.
We need to rewrite the numbers in form to get the rational numbers between 3 and 4.
So, after converting, we get.
We can further convert the rational numbers into lowest fractions.
On converting the fractions into lowest fractions, we get.
Therefore, six rational numbers between 3 and 4 are.
NCERT Solutions for Class 9 Maths Exercise 1.1
3. Find five rational numbers between.
Ans. We know that there are infinite rational numbers between any two numbers.
A rational number is the one that can be written in the form of, where p and q are
Integers and.
We know that the numbers can also be written as.
We can conclude that the numbers all lie between
We need to rewrite the numbers in form to get the rational numbers between 3 and 4.
So, after converting, we get.
We can further convert the rational numbers into lowest fractions.
On converting the fractions, we get.
Therefore, six rational numbers between 3 and 4 are.
NCERT Solutions for Class 9 Maths Exercise 1.1
4. State whether the following statements are true or false. Give reasons for your answers.
(i) Every natural number is a whole number.
(ii) Every integer is a whole number.
(iii) Every rational number is a whole number.
Ans. (i) Consider the whole numbers and natural numbers separately.
We know that whole number series is.
We know that natural number series is.
So, we can conclude that every number of the natural number series lie in the whole number series.
Therefore, we conclude that, yes every natural number is a whole number.
(ii) Consider the integers and whole numbers separately.
We know that integers are those numbers that can be written in the form of, where.
Now, considering the series of integers, we have.
We know that whole number series is.
We can conclude that all the numbers of whole number series lie in the series of integers. But every number of series of integers does not appear in the whole number series.
Therefore, we conclude that every integer is not a whole number.
(iii) Consider the rational numbers and whole numbers separately.
We know that rational numbers are the numbers that can be written in the form, where.
We know that whole number series is.
We know that every number of whole number series can be written in the form of as.
We conclude that every number of the whole number series is a rational number. But, every rational number does not appear in the whole number series.
Therefore, we conclude that every rational number is not a whole number.
Step-by-step explanation: