by Here we are giving some practice questions based on rational numbers.
1. Are the following statements are true or false? Give reason for your answers.
(i) every whole number is a natural numbers.
(ii) every integer is a rational number .
(iii)There are infinitely many rational numbers between any two given rational numbers.
(iv) 0 is a rational number.
(V)Every rational number is a whole number.
ANS. (i) False , beacuse ‘0’ is a whole number not a natural number.
(ii)True, because every integer can be expressed in the form
(iii) True
(iv) True , since we can write
(v)false
2. Find six rational numbers between 3 and 4.
Sol. To find a rational number between and
we can add
and
and divide the sum by 2 that is
lies between
and
.
Now let =3 and
=4 , then
=
is a number lying between 3 and 4 .
Next let =3 and
=
, then
is also a number lying between 3 and 4.
Rational no. between is
.
Proceeding in the same manner the six rational numbers between 3 and 4 are
,
.
3. Express the decimal in the form
where
and
are integers and
.
Sol. let . Since two digits are repeating, we multiply by
by 100 to get
So,
Therefore
i.e. , which gives
Hence , =
.
