Number system

Maths topic

Number system

Natural Numbers: 1, 2, 3, 4…..
Whole Numbers: 0, 1, 2, 3, 4…..
Integers: ….-2, -1, 0, 1, 2 …..
Rational Numbers: Any number which can be expressed
as a ratio of two integers for example a p/q format where
‘p’ and ‘q’ are integers. Proper fraction will have (p<q)
and improper fraction will have (p>q)
Factors: A positive integer ‘f’ is said to be a factor of a
given positive integer 'n' if f divides n without leaving a
remainder. e.g. 1, 2, 3, 4, 6 and 12 are the factors of 12.
Prime Numbers: A prime number is a positive number
which has no factors besides itself and unity.
Composite Numbers: A composite number is a number
which has other factors besides itself and unity.
Factorial: For a natural number 'n', its factorial is defined
as: n! = 1 x 2 x 3 x 4 x .... x n (Note: 0! = 1)

NOW YOU CAN TEST YOUR SELF

(i)

Every natural number is a whole number.

(ii)

Every integer is a whole number.

(iii)

Every rational number is a whole number.

Answer:

(i)

True; since the collection of whole numbers contains all natural numbers.

(ii)

False; as integers may be negative but whole numbers are positive. For example: -3

is an integer but not a whole number.

(iii)

False; as rational numbers may be fra ctional but whole numbers may not be. 

Test your self: :  is a 1/7   rational number but not a whole number.

State whether the following statements are true or false. Justify your answers.

(i)

Every irrational number is a real number.

(ii)

Every point on the number line is of the form , where m is a natural number.

(iii)

Every real number is an irrational number.

Answer:

(i)

True; since the collection of real numbers is made up of rational and irrational numbers.

(ii)

False;  as  negative  numbers  cannot  be  expressed  as  the  squa re  root  of  any  other

number.

(iii)

False; as real numbers include both rational and irrational numbers. Therefore, every

real number cannot be an irrational number.

test your self::

Are the square roots of a ll positive integers irrational? If not, give an example of the square

root of a number that is a rational number.

Answer:

If numbers such as are considered,

√4=2  √25=5  √36=6 etc

Then here,  2 and 3  are rational numbers. Thus, the square  roots of all positive integers

are not irrational.

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