## NUMBER SYSTEMS

*Very Short Q & A***Q1: Categorize the following numbers as**

(i) Natural Numbers

(ii) Whole Numbers

(iii) Integers

(i) Natural Numbers

(ii) Whole Numbers

(iii) Integers

**(iv) Rational Numbers**

**7, 3/2, 0, 2, -9/5, 1/4, -8**

Answer:

(i) Natural Numbers {2, 7}

(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?**

Answer: 0 (zero)

**Q3: Write the greatest negative integer.**

Answer: -1

**Q4: Name the smallest natural number.**

Answer: 1

**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 _________.

Answer:

(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 x**

^{2}is irrational but x^{4}is rational. Justify your answer by an example.Answer: let x = ∜2 then x

^{2}= √2 (irrational) but x

^{4 }= 2 is rational.

**Q9: Is 1 prime number or composite number?**

Answer: 1 is neither prime nor composite number.

**Q10: Is 571 prime?**

Answer: Approximate 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)

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