Find five rational numbers between 53 and 54.

Question

Find five rational numbers between 53​ and 54​.

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, so

(i) The rational number between

\frac{3}{5}

and

\frac{4}{5}

is average of

\frac{3}{5}

and

\frac{4}{5}

\frac{1}{2} (\frac{3}{5} + \frac{4}{5}) = \frac{1}{2} (\frac{3 + 4}{5}) = \frac{7}{10}

(ii) The second rational number between

\frac{3}{5}

and

\frac{4}{5}

can be calculated bye calculating the average of

\frac{3}{5}

and

\frac{7}{10}

\frac{1}{2} (\frac{3}{5} + \frac{7}{10}) = \frac{1}{2} (\frac{6 + 7}{10}) = \frac{13}{20}

(iii) The third rational number between

\frac{3}{5}

and

\frac{4}{5}

can be calculated by calculating the average of

\frac{7}{10}

and

\frac{4}{5}

\frac{1}{2} (\frac{7}{10} + \frac{4}{5}) = \frac{1}{2} (\frac{7 + 8}{10}) = \frac{15}{20}

(iv) The fourth rational number between

\frac{3}{5}

and

\frac{4}{5}

can be calculated by calculating the average of

\frac{3}{5}

and

\frac{13}{20}

\frac{1}{2} (\frac{3}{5} + \frac{13}{20}) = \frac{1}{2} (\frac{12 + 13}{20}) = \frac{25}{40}

(v) The fifth rational number between

\frac{3}{5}

and

\frac{4}{5}

can be calculated by calculating the average of

\frac{13}{20}

and

\frac{4}{5}

\frac{1}{2} (\frac{13}{20} + \frac{4}{5}) = \frac{1}{2} (\frac{13 + 16}{20}) = \frac{29}{40}

Then five rational are

\frac{7}{10}

,

\frac{13}{20}

,

\frac{15}{20}

,

\frac{27}{40}

and

\frac{29}{40}

Question Text	Find five rational numbers between $\frac{3}{5}$ and $\frac{4}{5}$ .
Answer Type	Text solution:1
Upvotes	150

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