## NUMBER SYSTEMS

Very Short Q & A

Q1: Categorize the following numbers as
(i) Natural Numbers
(ii) Whole Numbers
(iii) Integers
(iv) Rational Numbers
7, 3/2, 0, 2, -9/5, 1/4, -8

(i) Natural Numbers {2, 7}
(ii) Whole Numbers {0, 2, 7}
(iii) Integers {-8, 0, 2, 7}
(iv) Rational Numbers {-8, -9/5, 0, 1/4, 3/2, 2, 7}

Q2: What is the rational number which does not have reciprocal?

Q3: Write the greatest negative integer.

Q4: Name the smallest natural number.

Q5: Fill in the blanks.

(i) There are __________ many rational numbers between any two given rational numbers.
(ii) Every ___________ number is a whole number.
(iii) All counting numbers together with 0 constitute set of _______ numbers
(iv) All natural numbers together with 0 and negatives of all the natural numbers form the set of __________.
(v) The two rational numbers which are there own multiplicative inverses are _________.

(i) Infinitely
(ii) Natural
(iii) Whole
(iv) Integers
(v) {1, -1}

Q6 (mcq): Every rational number is

(a) a natural number
(b) an integer
(c) a real number
(d) a whole number

Answer: (c) a real number

Q7: Let x and y be rational and irrational numbers, respectively. Is x + y necessarily an
irrational number? Give an example in support of your answer.

Answer: Yes. Let x = 5 and y = √2, x + y = 5 +√2 (irrational number).

Q8: There is a number x such that x2 is irrational but x4 is rational. Justify your answer by an example.

Answer: let x = ∜2 then x2 √2 (irrational) but x= 2 is rational.

Q9: Is 1 prime number or composite number?

Answer: 1 is neither prime nor composite number.

Q10: Is 571 prime?

AnswerApproximate square root value of 571 is 24. Prime numbers < 24 are 2,3,5,7,11,13,17,19 and 23. None of these numbers divide 571. Thus 571 is a prime number.

Q11: Convert 0.9 into a rational number.

Answer: Let x = 0.9. Then x = 0.99999...
Multiplying by 10 on both sides we get,
10x = 9.9999... = 9 + 0.99999...  = 9 + x
⇒ 10x - x = 9
⇒ 9x = 9
⇒ x = 1
Thus 0.9 = 1 (rational number)

See Also Number Systems (NCERT Ex. 1.1)  