Number system facts 1 Flashcards
What are Natural numbers represented by ?
Natural numbers represented by N
What are Whole numbers represented by ?
Whole numbers represented by W
What are Integers represented by ?
Integers represented by Z or I
What are Rational numbers ?
A number ‘r’ is called a rational number, if it can be written in the form p/q where p and q are integers and q ≠ 0. Rational numbers can also be Terminating or
Non-terminating but repeating
Is every Integer a Rational number ?
Yes
How many Rational numbers are between any two given Rational numbers ?
Infinite
Every Rational number is ______________
A real number
Is zero a Rational number ?
Zero is a rational number as zero can be written as 0/1,0/2,0/3
What are Irrational numbers ?
A number ‘s’ is called irrational, if it cannot be written in the form p/q where p and q are integers and q ≠ 0 and its decimal expansion is non-terminating and non-repeating
What are Real numbers ?
The collection of all rational numbers and irrational numbers together make up what we call the collection of real numbers, which is denoted by R
State whether the following statements are true or false. Justify your answers
(i) Is every irrational number is a real number
(ii) Every point on the number line is of the form root m ,
where m is a natural number.
(iii) Every real number is an irrational number
(i) True, since collection of real numbers is made up of
rational and irrational numbers
(ii) False, no negative number can be the square root of any natural number
(iii) False, for example 2 is real but not irrational.
Are the square roots of all positive integers irrational? If not, give an example of the square root of a number that is a rational number
No For example, root of 4 = 2 is a rational number.
