Find five rational numbers between 3 and 4.

Question

Filo · Accepted Answer

Rational number is any number that can express in the form of

\frac{p}{q}

of two integers, where '

q

' cannot be zero.

i) First rational number between

3

and

4

can be calculated by finding average between them, which is

\frac{3 + 4}{2} = \frac{7}{2}

Now, we have three numbers i.e.

3, \frac{7}{2}

and

4

, so other remaining rational numbers can be calculated by taking average between

3

and

\frac{7}{2}

, and between

\frac{7}{2}

and

4

.

ii) Second rational number between

3

and

\frac{7}{2}

can be calculated by finding average between them.

\frac{\frac{7}{2} + 3}{2} = \frac{\frac{7 + 6}{2}}{2} = \frac{13}{4}

iii) The third rational number between

4

and

\frac{7}{2}

can be calculated by finding the average between them.

\frac{\frac{7}{2} + 4}{2} = \frac{\frac{7 + 8}{2}}{2} = \frac{15}{4}

iv) Similarly fourth rational number between

3

and

\frac{13}{4}

can be calculated by finding the average between them.

\frac{\frac{13}{4} + 3}{2} = \frac{\frac{13 + 12}{4}}{2} = \frac{25}{8}

v) Similarly, fifth rational number between

4

and

\frac{13}{4}

can be calculated by finding average between them.

\frac{\frac{13}{4} + 4}{2} = \frac{\frac{13 + 16}{4}}{2} = \frac{29}{8}

Then the rational numbers between

3

and

4

are

\frac{7}{2}, \frac{13}{4}, \frac{15}{4}, \frac{25}{8}, \frac{29}{8}

Question Text	Find five rational numbers between $3$ and $4$ .
Answer Type	Text solution:1
Upvotes	153

Find five rational numbers between $3$ and $4$ .