Question

In a school $5$ out of every $7$ children participated in ‘Save wildlife’ campaign organise by the school authorities. Based on the above information, answer the following question.

$\left(i\right)$ How many rational number between $5$ and $7$.
$\left(ii\right)$What fraction of students participated in the campaign?
$\left(iii\right)$State whether $\frac{5}{7}$ has terminating or non-terminating
and recurring decimal expansion?

Answer 1

Case (i)
ATQ,
As we know, there are infinite rational numbers between any two numbers.
Therefore, there are infinite numbers of rational numbers between 5 and 7.
Case (ii)
ATQ,
Total number of children $=7$
Also, total number of student participants in the campaign $=5$
Fraction $=\frac{Totalnumberofstudentsparticipated}{Totalnumberofchildren}=\frac{5}{7}$.
Therefore, fraction of students participated in the campaign $=\frac{5}{7}$.
Case$\left(iii\right)$
Decimal expansion of $\frac{5}{7}=$$0.714285$
Here, $0.714285$ is a non terminating and recurring decimal expansion.
Therefore, decimal form of $\frac{5}{7}$ i.e $0.714285$ is a non terminating and recurring decimal expansion.