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
(iv) True , since we can write
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
i.e. , which gives
Hence , =.