Get the Knowledge that sets you free...Science and Math for K8 to K12 students

Login / Register

Login to your account

Email
Password
×

Warning

Please Login to Read More...

Number Systems

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.
Thus, 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}.

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.
Place Value

The number system that we use in our daily life is the decimal number system. Decimal number system has base 10 as it uses 10 digits from 0 to 9, that is, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. By using these ten digits, the numbers are formed. For large numbers, commas (,) are used to separate digits into groups of three called periods.

In decimal number system, every digit has a place value on which the value of that particular digit depends. The place value indicates a digit's place or position in the entire number. Each place has a value of 10 times the place to its right. The value of numerals is determined by its positions. Place value starts counting from its right side. The place value chart is shown below:

Flash is Not Installed in Your System. Please Click here to Install. Close
Java is Not Installed in Your System. Please Click here to Install. Close