Number System

Introduction

    Numbers are the key elements of mathematics. Without them, you can’t imagine Math’s. Do you remember how you learn counting of objects during your early school days? The obvious answer is YES !

Natural Numbers

    Natural numbers: To count different or similar objects we need numbers, and these numbers are called counting numbers or natural numbers.

    1,2,3,4 _ _ _ and so-on are natural or counting numbers.

   Numbers are expressed in 2 ways:

• Notation: Writing any counting number in figure is called notation.
          Example: 436
• Numeration: writing the natural number in words is called numeration.
          Example: Four Hundred thirty six.

How to write Numbers?

    According to Hindu Arabic System, there are 10 symbols or digits to represent any number. They are: 0,1,2,3,4,5,6,7,8,9.

    Group of symbols or digits is called Number or Numeral. Place value method is used to represent any number.

    To write any numeral, always start from extreme right-hand side as Ones, Tens, Hundreds, Thousands and so-on.

    Note: While writing any number, always use units in singular form only.

    Period: While writing any number, periods(,) are required to separate different places.

• Ones, Tens and Hundreds places are taken together and they form Ones period.
• Thousands and Ten- Thousands places are taken together and they form Thousands period.
• Lakhs and Ten-Lakhs places are taken together and they form Lakhs period.
• Crores and Ten-Crores places are taken together and they form Crores period.

Face Value of a digit in a Number

    The exact value of the digit itself in a number is called its face value.

    Note: for face value, position of a digit in a number does not matter.

    Example: In 46392,

• The face value of 3 is 3.
• The face value of 6 is 6.
• The face value of 4 is 4 and so-on.

Place Value of a digit in a Number

    Place value is defined as the place where digit is placed in a number. It is calculated as:

    Place value of digit = Face value of digit in number * Value of place.

    Example: In 46392,

• The place value of 3 is 3*100= 300.
• The place value of 6 is 6*1000= 6000.
• The place value of 2 is 2*1=2 and so-on.

Whole Number

    Counting numbers with 0 are whole numbers.

    0,1,2,3……. so-on.

Note: 

• All natural numbers are whole numbers.
• 0 is only whole number which is not a natural or counting number.

Successor of a number

    Successor of a number is the number or value that is placed immediately after it. It is 1 more than a number.

    Successor is calculated by adding 1 to a number.

    Example: Successor of 92 is 93.

Predecessor of a number

    Predecessor is that number which comes before the number. It is 1 less than the number.

    Predecessor is calculated by subtracting 1 from the number.

    Example: Predecessor of 92 is 91.

Comparison of Numbers

    To compare two numbers, following steps should be followed:

• Step 1: Count the number of digits in each number. The number with more number of digits is the greatest one.
• Step 2: If number of digits in each number is same then:
  • Compare left most digit of each number.
  • If left most digit of both numbers is same then proceed further with next digits. Repeat this step until you find greater digit at same place in both numbers. Number with greater digit is the greatest.
  • If left most digit of both numbers is different, the number with greater digit is the greatest.

Word Problems

    A problem expressed in few sentences is called word problem. These are based on real life scenarios. Word problems can be solved by applying different mathematical concepts and calculations. It helps the learners to experience different operations like addition, subtraction, multiplication and division on large numbers.

Approximation

    One must know how to round off a number to nearest ten, hundred, thousand etc. before applying approximation.

1. How to round off a number to nearest Ten?
   • Step 1: Check Ones digit place of a number
   • Step 2: If digit at Ones place is less than 5, then replace the digit at Ones place with 0 and keep other digits same as they are.
2. How to round off a number to nearest Hundred?
   • Step 1: Check Tens digit place of a number
   • Step 2: If digit at Tens place is less than 5, then replace the digit at Tens  and Ones place with 0 and keep other digits same as they are.
3. How to round off a number to nearest Thousand?
   • Step 1: Check Hundreds digit place of a number
   • Step 2: If digit at Hundreds place is less than 5, then replace the digit at Hundreds , Tens  and Ones place with 0 and keep other digits same as they are.

International System of Numeration

International System of Numeration is divided into different periods of Ones, Thousands, Millions etc.

1. Ones, Tens and Hundreds places are taken together and they form Ones period.
2. Thousands, Ten Thousands, Hundred Thousands places are taken together and they form Thousands period.
3. Millions, Ten Millions, Hundred Millions places are taken together and they form Millions period.

Number System Tutorial