LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

NUMBER SYSTEM

__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**