Q1. Is zero a rational number? Can you write it in the form p/q where p and q are integers and q ≠ 0?
Ans: 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
Taking the case of '0',
Yes, zero is a rational number.
0 =
Example :
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.
Q2. Find six rational numbers between 3 and 4.
Ans: We can find any number of rational numbers between two rational numbers. 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)
We can choose 6 rational numbers as: and
Q3. Find five rational numbers between 3/4 and 4/5.
Ans: There are infinite rational numbers between 3/4 and 4/5.
Since we need to make the denominators same first, then
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)
∴ Five rational numbers between areand
Q4. State whether the following statements are true or false. Give reasons for your answers.
(i) Every natural number is a whole number.
Ans: True
Natural Numbers: Natural numbers are set of numbers that contain numbers from 1 to infinity. Set of natural numbers is represented as N= {1, 2, 3…….}.
Whole numbers: Numbers starting from 0 to infinity (without fractions or decimals)
Set of Whole numbers is represented as W= 0,1,2,3….
As all the natural numbers comes in the set of whole numbers. Hence, every natural number is a whole number.
(ii) Every integer is a whole number.
Ans: 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.
Ans: 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 include whole numbers as well as negative numbers.
Every whole number is rational, however, every rational number is not a whole number.
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1. What is the number system and why is it important in mathematics? |
2. What are the different types of numbers in the number system? |
3. How do you represent rational numbers on a number line? |
4. Can you give examples of rational and irrational numbers? |
5. What is the significance of understanding the properties of numbers in the number system? |
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