ICSE Class 6 Maths Chapter 1 Number System revision notes

Concept 1: Hindu – Arabic System of Numeration

In this system, we use ten symbols namely: 0, 1, 2,3,4,5,6,7,8 and 9 to represent any number. These symbols are called digits.

Concept 2: Place value and Face value

1. Place value of a digit in a number depends on the place it occupies in the number
2. The face value of a digit is the digit itself
3. ‘0’ is the only digit whose face value and place value both are same, i.e. the face value of 0 is 0 and place value of 0is also 0.

Example 1. Find the place value of all the digits in the number 35268
Soln. In the number 35268, we have
• The place value of 8 = 8 x 1 = 8
• The place value of 6 = 6 x 10 = 60
• The place value of 2 = 2 x 100 = 200
• The place value of 5 = 5 x 1000 = 5000
• The place value of 3 = 3 x 10000 = 30000

Expanded form of a number: A number is expanded on the basis if the place values of the digits. For instance,
Number = unit’s place x (unit) + ten’s place x (10) + hundredth place x (100) + thousand’s place x (1000) + … and so on.
Comparison of 2 numbers: To decide which one is bigger, remember the following:
1) Of the 2 numbers the number having more digits is bigger
2) If 2 numbers have an equal number of digits, then the number having the larger digit in the leftmost place is bigger. If the digit in the leftmost place are equal then the number having the larger digit in the place on the right of the equal digits is bigger, and so on

Example 2. Compare the numbers:

1. 8325 and 14103
2. 60714 and 52130
   Soln.
   1) The first number has four digits while the second has five digits. So, the second number is bigger.
   2) The 2 numbers have an equal number of digits, however, 6<5. So, 60714 is the biggest number.

Concept 3: Natural number and Whole number

Natural number and Whole number

Natural number: The counting number 1, 2,3,4,5,6, …, are called natural numbers.
1 is the first and the smallest natural number. Any natural number can be obtained by adding 1 to its previous natural number.
There is no last or largest natural number. Therefore, there are infinite whole numbers.

Whole number: The number ‘0’ altogether with natural number, called whole numbers, i.e. 0,1,2,3,4,5, … etc. are called whole numbers
0 is the first and the smallest whole number
There is no last or largest whole number. Therefore, there are infinite whole numbers.
Examples:

1. Find the face values of all the digits in the number 83245.
   Soln. In the number 83245
   • The face value of 5 is 5.
   • The face value of 4 is 4.
   • The face value of 2 is 2.
   • The face value of 3 is 3.
   • The face value of 8 is 8.

1. Find all the possible three digit numbers using the digits 1,3,5 taking each diggings
   Keeping 1 at the ones place the numbers formed are 751 and 571
   Keeping 5 at the ones place, the numbers formed are 157 and 517
   So, the required numbers are 751, 571, 175, 715, and 157,517.