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

## Number Systems Exercise Ex. 1.1

### Solution 1

Yes zero is a rational number as it can be represented in the   form,  where p and q are integers and q  0 as  etc.

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   .

### Solution 3

There are infinite rational numbers in between 3 and 4.
3 and 4 can be represented as respectively.

Now rational numbers between 3 and 4 are

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.

### Solution 4

There are infinite rational numbers between

Now rational numbers between are

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) False

(ii) True

(iii) False

(iv)True

(v) False

(vi) False

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

## Number Systems Exercise Ex. 1.4

### Solution 3(x)

As decimal expansion of this number is non-terminating non recurring. So it is an irrational number.

### Solution 3(xi)

Rational number as it can be represented in   form.

### Solution 3(xii)

0.3796

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

### Solution 3(xiii)

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

### Solution 10

3 irrational numbers are -
0.73073007300073000073 ... ... ...
0.75075007500075000075 ... ... ...
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

Irrational number between two numbers x and y

## Number Systems Exercise Ex. 1.5

### Solution 1

(i) Real, rational, irrartional.

(ii) terminating, repeating.

(iii) terminating, non-terminating and reccuring.

(iv) rational, an irrational.

(i) True

(ii) True

(iii) False