# RD SHARMA Solutions for Class 9 Maths Chapter 1 - Number Systems

## Chapter 1 - Number Systems Exercise Ex. 1.1

**Concept Insight:**Key idea to answer this question is "every integer is a rational number and zero is a non negative integer". Also 0 can be expressed in form in various ways as 0 divided by any number is 0. simplest is .

3 and 4 can be represented as respectively.

**Concept Insight:**Since there are infinite number of rational numbers between any two numbers so the answer is not unique here. The trick is to convert the number to equivalent form by multiplying and dividing by the number atleast 1 more than the rational numbers to be inserted.

**Concept Insight**: Since there are infinite number of rational numbers between any two numbers so the answer is not unique here. The trick is to convert the number to equivalent form by multiplying and dividing by the number at least 1 more than the rational numbers required.

Alternatively for any two rational numbers a and b, is also a rational number which lies between a and b.

(i) Every whole number is a natural number.

(ii) Every integer is a rational number.

(iii) Every rational number is an integer.

(iv) Every natural number is a whole number.

(v) Every integer is whole number.

(vi) Every rational number is whole number.

(ii) True

(iii) False

(iv)True

(v) False

(vi) False

## Chapter 1 - Number Systems Exercise Ex. 1.2

(i)

(ii)

(iii)

(iv)

(v)

(vi)

## Chapter 1 - Number Systems Exercise Ex. 1.3

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

## Chapter 1 - Number Systems Exercise Ex. 1.4

Rational number as it can be represented in form.

As decimal expansion of this number is terminating, so it is a rational number.

0.73073007300073000073 ... ... ...

0.79079007900079000079 ... ... ...

**Concept Insight: **There is infinite number of rational and irrational numbers between any two rational numbers. Convert the number into its decimal form to find irrationals between them.

Alternatively following result can be used to answer

## Chapter 1 - Number Systems Exercise Ex. 1.5

(i) Every point on the number line corresponds to a ___ number which may be either ____ or_____.

(ii) The decimal form of an irrational number is neither ______ nor ______.

(iii) The decimal representation of a rational number is either ____ or _____.

(iv) Every real number is either ______ number or ______ number.

(ii) terminating, repeating.

(iii) terminating, non-terminating and reccuring.

(iv) rational, an irrational.

Find whether the following sentences are true or false:

(i) Every real number is either rational or irrational.

(ii) is an irrational number.

(iii) Irrational numbers cannot be represented by points on the number line.

(i) True

(ii) True

(iii) False

## Chapter 1 - Number Systems Exercise Ex. 1.6

## Chapter 1 - Number Systems Exercise 1.40

Which one of the following is a correct statement?

(a) Decimal Expansion of a Rational number is terminating.

(b) Decimal Expansion of a Rational number is Non-terminating.

(c) Decimal Expansion of a irrational number is terminating.

(d) Decimal Expansion of a irrational number is Non-terminating and Non-Repeating.

Which one of the following statement is true?

(a) The sum of two irrational numbers is always an irrational number.

(b) The sum of two irrational numbers is always a rational number.

(c) The sum of two irrational numbers may be a rational number or an irrational number

(d) The sum of two irrational numbers is always an Integer.

Which of the following is a correct statement?

(a) Sum of two irrational numbers is always irrational.

(b) Sum of a rational and irrational number is always irrational.

(c) Square of an irrational number is always a Rational number.

(d) Sum of two Rational numbers can never be an integer.

Which of the following statements is true?

(a) Product of two irrational numbers is always irrational

(b) Product of a rational and an irrational number is always irrational

(c) Sum of two irrational numbers can never be irrational

(d) Sum of an integer and a rational number can never be an integer

Which of the following is irrational?

Which of the following is irrational?

Which of the following is rational?

The number 0.318564318564318564......... is:

(a) a natural number

(b) an integer

(c) a rational number

(d) an irrational number

(a) always a natural number

(b) always an rational number

(c) always an irrational number

(d) sometimes a natural number and sometimes an irrational number.

## Chapter 1 - Number Systems Exercise 1.41

Which of the following numbers can be represented as non-terminating repeating decimals?

Every point on a number line represents:

(a) a unique real number

(b) a natural number

(c) a rational number

(d) an irrational number

Which of the following is irrational?

(a) 0.15

(b) 0.01516

(c)

(d) 0.5015001500015

An irrational number between 2 and 2.5 is

(a) 3

(b) 2

(c) 4

(d) 5

## Chapter 1 - Number Systems Exercise 1.42

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