1. Is zero a rational number? Can you write it in the form pq, 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 pq , where p and q are integers and q ≠0.
Zero can be written in the form 0,01,02,03,04,0-1,0-2,0-3,0-4,...........
Hence, zero 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.
Example : 3×(77)=217 and 4×(77)=287.
The numbers in between 217 and 287 will be rational and will fall between 3 and 4.
Hence, 227,237,247,257,267,277are the 6 rational numbers between 3 and 4.
3. Find five rational numbers between 35 and 45.
solution :
There are infinite rational numbers between 35 and 45.
To find out 5 rational numbers between 35 and 45.
we will multiply both the numbers 35 and 45
with 1010 (or any number greater than 5)
Example : (35)×(1010)=3050 and (45)×(1010)=4050.
The numbers in between 3050 and 4050 will be rational and will fall between 35 and 45.
Hence, 3150,3250,3350,3450,3550 are the 5 rational numbers between 35 and 45.
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.
solution :
(i) Every natural number is a whole number.
TRUE
Natural numbers : Numbers starting from 1 to infinity
Example : Natural numbers= 1, 2, 3, 4, 5, 6, 7, ...............,∞.
Whole numbers : Numbers starting from 0 to infinity
Example : Whole numbers= 0, 1, 2, 3, 4, 5, 6, 7,....................., ∞.
Or, we can say that whole numbers have all the elements of natural numbers and zero.
Hence, Every natural number is a whole number.
(ii) Every integer is a whole number.,
FALSE
Integers : Integers are set of numbers that contain positive,negative and 0.
Example : integers are -∞, .........-6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, ........, ∞.
Whole numbers : Numbers starting from 0 to infinity.
Example : Whole numbers are 0, 1, 2, 3, 4, 5, .............,∞.
Or, we can say that every integers are not whole numbers.
Hance, Every integer is not a whole number.
(iii) Every rational number is a whole number.
FALSE
Rational numbers : All numbers in the form pq, where p and q are integers and q ≠0.
Example : Rational numbers are 0,-15,27,0-9,-17,...............,∞.
Whole numbers : Numbers starting from 0 to infinity.
Example : Whole numbers and 0, 1, 2, 3, 4, 5, 6, 7, .............., ∞.
Or, we can say that every Rational numbers not Whole numbers.
Hence, All rational numbers are not whole numbers.
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