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Decimal Number System

Natural Numbers

The numbers which are used for counting are called natural numbers or counting numbers.
The natural numbers set is an infinite set and is denoted by N.
It is represented as, N = {1, 2, 3, 4, 5, 6, 7, 8, . . .}

Representation of natural numbers on number line:
Draw a line. Mark points at equal intervals of length (say 1 unit), as shown below.
Label these points as 1, 2, 3, 4, 5, . . .
Then, these points will represent the natural numbers 1, 2, 3, 4, 5, . . . respectively on the number line.
The arrowhead at one end of the number line indicates the continuation of these numbers indefinitely.

The number line shows the order of natural numbers.
A number that appears to the left of a given number is less than (<) the given number.
A number that appears to the right of a given number is greater than (>) the given number.
So we can conclude that 1 < 2 < 3 < 4 < 5 . . .

Example: Are these subsets of natural numbers set (N) ?
a) No. of days in each month of a calendar year.
b) Sum of numbers when two dice are cast.
c) Points scored in wooden pinball game (Runner duck) say with 6 strikes.
For solution refer to adjacent table.
Whole Numbers

If we add '0' (zero) to the set of natural numbers, then those set of numbers become whole numbers.
The whole numbers set is an infinite set and is denoted by W.
Thus, W = {0, 1, 2, 3, 4, 5, 6, 7, 8, . . .} = N ∪ {0}
where ∪ represents "union" of two sets.

Representation of whole numbers on number line:
Like natural numbers, we may represent whole numbers by points on the number line, as shown below:

Points to remember
• Every natural number is a whole number.
• '0' is a whole number which is not a natural number.
Example: In a game of cricket, are these subsets of natural numbers set (N) or whole numbers set (W) ?
a) Runs scored by a batsman in several innings.
b) Runs given away by a bowler in an over.
For solution refer to adjacent table.
Thermometer A thermometer (a word derived from the Greek thermos, meaning “hot” and metron, “measure”) is an instrument used to measure outside and inside temperature, body temperature, oven temperature and food temperature. Thermometers use number lines to measure the temperature.
The Real Number Line

A value that represents a quantity along a continuous line is defined as a real number. The set of all real numbers is usually denoted by ‘R’.

A straight line on which real numbers can be pictured as points is called a real number line, or simply a number line.
To construct a real number line, we draw a straight line and label any convenient point with the number '0', called the origin.
Now we choose any convenient length and use it to locate other points.
Points to the right of '0' correspond to the positive real numbers and points to the left of '0' correspond to the negative real numbers.

The point on a real number line that corresponds to a real number is called the graph of the number. Drawing the point is called graphing the number or plotting the point.
The number that corresponds to a point on a real number line is called the co-ordinate of the point.
The numbers on a number line increase from left to right. When graphing two numbers on a number line, the number to the right is always greater.

Representation of integers on number line

Draw a line. Mark a point on it and label it as '0'. Set off equal distances on both sides of the point representing '0'.
Label the points lying on the right of '0' as 1, 2, 3, 4, 5, . . .
and those lying on the left of '0' as –1, –2, –3, –4, –5, . . .

Representation of integers on number line

The arrowheads on both sides of the number line indicate the continuation of integers indefinitely on each side.

Absolute value of an integer:
The absolute value of an integer is the numerical value without regard to whether the sign is negative or positive.
Ex: The absolute value of +21 is 21 and the absolute value of –21 is also 21.

On a number line, the absolute value is the distance between the number and zero (0).
The symbol for absolute value is two vertical bars on either side of the number such as | -7 | = 7
Note: Read "| -7 | = 7" as "absolute value of -7 is 7".