Class 9 Chapter 1
All questions and solutions
Q.1. Is zero a rational number? Can you right it in the form p/q, where p and q are integers and q≠0?
Ans. Yes, zero is rational number. It can be written in the form of p/q. Like this:- 0/1, 0/2, 0/3, 0/5, 0/9……
Q. 2. Find six rational numbers between 3 and 4.
Ans. There are many rational numbers between 3 and 4. These may be written as 3/1 and 4/1. We have to find denominator more than sum of both numbers 3 and 4. Now we will multiply both, numerator and denominator by a number more than 3+4=7.
3×7/1×7 =21/7 and 4×7/1×7=28/7
Now the numbers are 21/7 and 28/7.
All numbers between 21/7 and 28/7 are the required numbers.
22/7, 23/7, 24/7, 25/7, 26/7, 27/7 are between 3 and 4 and all these numbers are rational numbers.
Q. 3. Find five rational numbers between 3/5 and 4/5.
Ans. There are many rational numbers between 3/5 and 4/5.
To find 5 rational numbers between these numbers, we have to multiply these numbers with more than 6 or above.
3×7/5×7= 21/35 and 4×7/5×7=28/35
Now the numbers are 21/35 and 28/35.
All numbers between these numbers are the required numbers.
22/35, 23/35, 24/35, 25/35, 26/35, 27/35, 28/35. All these rational numbers are between 3/5 and 4/5.
Q. 4. State whether the following statements are true or false. Give reasons for your answers.
(i) Every natural number is a whole number.
Ans. True, because numbers started from 1 to infinity are Natural numbers. Fractions and decimals are not Natural numbers.
Natural numbers- 1,2,3,4,5…… to infinity
Whole numbers are started form 0 to infinity and fractions and decimals are not Natural numbers.
Whole numbers- 0,1,2,3,4,5……. to infinity.
Thus we can say that all Natural numbers are included in Whole numbers but Whole numbers are not included in Natural numbers because there is a defference of ‘0’ between them.
(ii) Every integer is a whole number.
Ans. False, because Integers include negative, positive and zero but Whole numbers do not include negative numbers.
(iii) Every rational number is a whole number.
Ans. False, because every rational number is not a whole number but every whole number is a rational number.
Rational numbers are all numbers in form of p/q where p and q are integers and q≠0, include 0,2/3,1/2,0/1,0/8,0, 2,3,9.,-2/3,-8,-9,-6…..
But whole numbers include 0,1,2,3,4,5,6,7……to infinity excluding fractions and decimals.