Number System
The number only can be described by a digit which is 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Any number can be made by digit from 0, 1,……….,8, 9.
1) To count any type of things or object usually we used the number which is called Natural Numbers (N).
You would like to know that, the the set of natural numbers is N = { 1, 2, 3,…………… }
2) Set of Whole numbers start with zero ‘0’ along with natural numbers is looks like = { 0, 1, 2, 3,……… }
3) Also we have learn about Place Value, Face Value, Etc. The Place value of the digit or number is called a numeral consist of more than one digit and each digit takes value according to the place it occupied.
For Example – in numeral 534 place value of the 5 is five hundred and the place value of 3 is Three Tens, and in another numeral 2349, the place value of 2 is Two Thousands and the place value of 9 is Nine Ones.
4) Actual value of any digit of any numeral is called of his own face value.
For Example – In numeral 794, the face value of 9 is Nine and the face value of 7 is Seven.
Exercise-1) Write all possible four-digit numbers using the digits 2, 4, 8 & 6 without repetition of the digit.
2 digit unit place => 2486, 2864, 2684, 2846, 2468, 2648
4 digit unit place => 4286, 4862, 4682, 4628, 4826, 4268,
8 digit unit place => 8246, 8264, 8426, 8462, 8624, 8642
6 digit unit place => 6248, 6284, 6428, 6482, 6824, 6842
Exercise.2) Write all possible four-digit numbers using the digits 4, 8 & 6 without repetition of the digit.
4 digit unit place => 486, 468
8 digit unit place => 846, 864
6 digit unit place => 648, 684
Exercise- 3) How many whole digit number has a) two-digit number and b) three-digit number and c) one-digit number ?
Ans.) a) The two digit whole number is => 10, 11, 12, 13,……………..,96, 97, 98, 99
The number of two digit numbers = 99 – (10-1) = 99 – 9 = 90
b) Three digit whole numbers are = > 100, 101, 103, 104, 105, ………………, 996, 997, 998, 999
The number of three digit numbers are = 999 – (100-1) = 999 – 99 = 900
c) one digit whole numbers are => 0, 1, 2, 3, 4,……………..,8, 9
The numbers of one digit numbers are = 9 – ( 0-1) = 9 – (-1) = 10
Exercise- 4) What are the greatest and smallest four-digit numbers that can be formed by using the digits 4, 2, 1, 5 without repeating any of the digits in a number ?
Ans.) The digit 4, 2, 1, 5 in descending order are = 5, 4, 2, 1
So, the greatest four-digit number is = 5421
And, the digit 4, 2, 1, 5 in Ascending order are = 1, 2, 4, 5
So, the smallest four-digit number is = 1245
Exercise-5) What are the greatest and smallest five-digit numbers that can be formed by using the digits 3, 7, 0, 2, 1 without repeating any of the digits in a number ?
Ans.) The digit 3, 7, 0, 2, 1 in descending order are = 7, 3, 2, 1, 0
So, the greatest five-digit number is = 73210
And, the digit 3, 7, 0, 2, 1 in ascending order are = 0, 1, 2, 3, 7, since placing the digit 0 in the leftmost place would yield a four-digit number, so we place it in the next place
So, the smallest five-digit number is = 10237
Exercise-6) What is the smallest four-digit number that can be written when the digits are a) repeated and b) not repeated?
Ans.) a) The two smallest digits are 0 and 1
The thousands place cannot have 0, because then the number would have only three digits, so, I will occupy the thousands place and the next three places will be occupied by 0
Hence the required number is = 1000
b) The four smallest digits are 0, 1, 2, 3 ; 0 can’t occupy the thousands place
Hence the required number is = 1023