Is zero a rational number? Can you write it in the form p/q, where p and q are integers and q ≠ 0?
Yes. Zero is a rational number as it can be represented as 0/1 or 0/2.
There are infinite rational numbers in between 3 and 4.
3 and 4 can be represented as 24/8 and 32/8 respectively.
Therefore, six rational numbers between 3 and 4 are
25/8, 26/8, 27/8, 28/8, 29/8, 30/8.
There are infinite rational numbers in between 3/5 and 4/5
3/5 = 3×6 / 5×6 = 18 / 30
4/5 = 4×6 / 5×6 = 24/30
Therefore, five rational numbers between 3/5 and 4/5 are
19/30, 20/30, 21/30, 22/30, 23/30.
State whether the following statements are true or false. Give reasons for your answers.
(i) Every natural number is a whole number.
ANS: True, since the collection of whole numbers contains all natural numbers.
(ii) Every integer is a whole number.
ANS: False, as integers may be negative but whole numbers are always positive.
(iii) Every rational number is a whole number.
ANS: False, as rational numbers may be fractional but whole numbers may not be.
(i) Every irrational number is a real number.
ANS: True, since the collection of real numbers is made up of rational and irrational numbers.
(ii) Every point on the number line is of the form√m, where m is a natural number.
ANS: False, since positive number cannot be expressed as square roots.
(iii) Every real number is an irrational number.
ANS: False, as real numbers include both rational and irrational numbers. Therefore, every real number cannot be an irrational number.