Examination Tension

NUMBER SYSTEM

In Hindu Arabic System, we use ten symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 called digits to represent any number. This is the decimal system where we use the numbers 0 to 9. 0 is called insignificant digit whereas 1, 2, 3, 4, 5, 6, 7, 8, 9 are called significant digits.
A group of figures, denoting a number is called a numeral. For a given numeral, we start from extreme right as Unit's place, Ten's place, Hundred's place and so on.
We represent the number 50,78,69,324 as shown below

We read it as Fifty crores, seventy -eight lacs, sixty nine thousands ,three hundred and twenty four.
In this numeral:
The Place value of 4 is 4 × 1 = 4
The place value of 2 is 2 × 10 = 20
The place value of 3 is 3 × 100 = 300
The place value of 9 is 9 × 1000 = 9000 and so on.
The place value of 9 is 6 × 10000 = 60000 and so on
The face value of a digit in a number is the value itself wherever it may be.
Thus, the face value of 7 in the above numeral is 7. The face value of 6 in the above numeral is 6 and so on.

NATURAL NUMBERS

Counting numbers 1, 2, 3, 4, 5, ... are known as natural numbers.
The set of all natural numbers can be represented by N = {1, 2, 3, 4, 5, ...}.

WHOLE NUMBERS

If we include 0 among the natural numbers, then the numbers 0, 1, 2, 3, 4, 5, ... are called whole numbers.
The set of whole numbers can be represented by W = {0,1,2,3,4,5, ...}
Clearly, every natural number is a whole number but 0 is a whole number which is not a natural number.

INTEGERS

All counting numbers and their negatives including zero are known as integers.
The set of integers can be represented by
Z or I = {... −4, ―3, ―2, ―1, 0, 1, 2, 3, 4 ......}

POSITIVE INTEGERS

The set I+ = {1, 2, 3, 4, ....} is the set of all positive integers. Clearly, positive integers and natural numbers are synonyms.

NEGATIVE INTEGERS

The set { ―1, ―2, ― 3, ...} is the set of all negative integers. 0 is neither positive nor negative.

NON-NEGATIVE INTEGERS...