Question

EXERCISE 1.1
1.
Is zero a rational number? Can you write it in the form , where p and q are integers
9
and q +0?
970
2. Find six rational numbers between 3 and 4.
3 4
3. Find five rational numbers between
and
5 5
4. State whether the following statements are true or false. Give reasons for your answers.
(i) Every natural number is a whole number.
(ii) Every integer is a whole number.
(iii) Every rational number is a whole number.​

Answer 1

Question:-1

Is zero a rational number? Can you write it in the form p/q, where p and q are integers and q ≠ 0

Answer:-

Yes, zero is a rational number

Zero( 0 ) can be written in the form of p/q

i . e .0 = 0/1

Here, p = 0 and q = 1 are integers and q = 1 ≠ 0

Question:-2

Find six rational numbers between 3 and 4

Answer:-

We know that, a rational number lies between middle of two numbers can be found dividing the sum of given numbers by 2

This means a rational number between given two numbers can be found by calculating the average of given numbers

Here, given numbers = 3 and 4

( a ) 1st rational number between 3 and 4

Average of 3 and 4

⇒$\frac{3+4}{2}$

⇒$\frac{7}{2}$

( b ) 2nd rational number between 3 and 4

Average of $\frac{7}{2}$ and 4

⇒$\frac{(\frac{7}{2}+4)}{2}$

⇒$\frac{(\frac{7+8}{2})}{2}$

⇒$\frac{15}{2}/2$

⇒$\frac{15}{2×2}$

⇒$\frac{15}{4}$

( c ) 3rd rational number between 3 and 4

⇒$(\frac{15}{4}+4)/2$

⇒$\frac{((15+16)4)}{2}$

⇒$(\frac{31}{4})/2$

⇒$\frac{31}{4×2}$

⇒$\frac{31}{8}$

( d ) 4th rational number between 3 and 4

⇒$(\frac{31}{8}+4)/2$

⇒$(\frac{31+32}{8})/2$

⇒$(\frac{63}{8}/2$

⇒$\frac{63}{8×2}$

⇒$\frac{63}{16}$

( e ) 5th rational number between 3 and 4

⇒$(\frac{63}{16}+4)/2$

⇒$(\frac{63+64}{16})/2$

⇒$(\frac{127}{16})/2$

⇒$\frac{127}{16×2}$

⇒$\frac{127}{32}$

( f )6th rational number between 3 and 4

⇒$(\frac{127}{32}+4)/2$

⇒$(\frac{127+128}{32})/2$

⇒$(\frac{255}{32}/2$

⇒$\frac{255}{32×2}$

⇒$\frac{255}{64}$

Thus, $\frac{7}{2},\frac{15}{4},\frac{31}{8},\frac{63}{16},\frac{127}{32} and \frac{255}{64}$ are six rational numbers between 3 and 4.

Question:-3

Find five rational numbers between $\frac{3}{5} and \frac{4}{5}$

Answer:-

(a) first rational number

⇒$(\frac{3}{5}+\frac{4}{5})/2$

⇒$(\frac{3+4}{5}/2$

⇒$\frac{7}{5}/2$

⇒$\frac{7}{5×2}$

⇒$\frac{7}{10}$

( b ) second rational number

⇒$(\frac{7}{10}+\frac{4}{5})/2$

⇒$(\frac{7+8}{10})/2$

⇒$(\frac{15}{10})/2$

⇒$\frac{15}{10×2}$

⇒$\frac{15}{20}-------( 1 )$

( c )third rational number

[from equation ( 1 )]

⇒$(\frac{15}{20}+\frac{4}{5})/2$

⇒$(\frac{15+16}{20})/2$

⇒$(\frac{31}{20})/2$

⇒$\frac{31}{20×2}$

⇒$\frac{31}{40}$

( d )forth rational number

⇒$(\frac{31}{40}+\frac{4}{5})/2$

⇒$(\frac{31+32}{40})/2$

⇒$(\frac{63}{40})/2$

⇒$\frac{63}{40×2}$

⇒$\frac{63}{80}$

( e ) fifth rational number

⇒$(\frac{63}{80}+\frac{4}{5})/2$

⇒$(\frac{63+64}{80})/2$

⇒$(\frac{127}{80})/2$

⇒$\frac{127}{80×2}$

⇒$\frac{127}{160}$

Thus, $\frac{7}{10},\frac{15}{20},\frac{31}{40},\frac{63}{80} and \frac{127}{160}$ five rational number between 3/5 and 4/5

Question:-4

State whether the following statements are true or false. Give reason for your answers?

Answer:-

( 1 ) Every natural number is a whole number

Answer:- True

Reason:-Natural numbers along with zero are called whole numbers

Thus, every natural number is a whole number

( 2 ) Every integer is a whole number

Answer:- False

Reason:-All natural numbers, zero and negative of counting numbers collectively from Integers, while whole numbers are natural numbers along with zero.

Since, whole numbers do not contain negative numbers while integers can be negative too.

Thus, every integer is not a whole number

( 3 )Every rational number is a whole number

Answer:- False

Reason:- Whole numbers do not contain fractions while rational numbers contain fraction too. Thus, every rational number is not a whole number

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