In this series first we learn what is unit digit and how we find unite digit.

1) Unite digit:- First we must know that what is the unit digit?

Unit digit mean the first digit of any number is called unit digit.

Number System Examples with Solutions

Example:- We have given a number 2523 what is the unit digit in this number?

Solution:- in this number unit digit is 3. Where 3 is the first digit of 2523 so 3 is the unit digit.

Next how find the unit digit?

1> If we have given any series in the addition form in this case we take unit digit of all number and then do sum of all unite digit.

Number System Examples Solutions

Example:- we have given the series 258 + 325 + 256 find the unit digit.

Solution:- We take the unit digit of all number and take the sum of them.

8 + 5 + 6 = 19

So unite digit of this series is 9.

Number System Examples Solutions

2> If question is given in multiple form then we take the unit digit of all number and then take their multiple.

Example:- 252 * 328 * 657 * 234 find the unite digit.

Solution:- we take unite digit of all number then multiply them.

Unite digit of all number    2 * 8 * 7 * 4 = 16 * 28 = 8* 6 = 48

So unite digit is 8.

3> If we have given the number in power form then we divide the power of number by 4 and which is come remainder take the same power of unite digit.

Example:- 78624⁹⁴ find the unite digit of this number.

Solution:- We divide 94 by 4 because 94 is the power of 78624.

When we divide 94 by 4 we get the remainder 2.

94 = 4 * 23 + 2

Now we take the 2 power of unite digit of 78624.

4² = 16

So the unite digit is 6.

Some Important Rules:-

Number System Rules

Rule(1):- If we have given the series in the multiple form and in that any odd number come with 5 then always unite digit of that series will 5.

Number System Rules

Rule(2):- If any series given multiple form and in that series any even number come with 5 then unite digit of that series will 0.

Rule(3):- If we have given series in multiple form and in that series odd and even numbers are come together with 5 then unite digit will 0.

Number System Rules

Rule(4) If we have given the number in power form in that case unite digit of number is odd or even and after divide of power by 4 remainder comes 0 then if unite digit is even then unite digit of solution will 6. And if unite digit of number is odd then unit digit of solution will 1 (except 5).

 

Digit:- Generally we use  ten numbers to represents  a big number they are 0,1,2,3,4,5,6,7,8,9 .

Example:- 11,12,100,1999………….

Representations of Numbers:-

When we write any number then we represent it right to left as first digit called unit, second digit called ten, third digit called hundreds………

Example: 

Value of Digit in numbers:-

Value of digit in numbers are two types.

1):-Face value

2):-Place value:-

1:- Face value of digit:- In a given number face value of a given digit will be same as its personal value.

Example:- 854632 in this number face value of 4 will be 4 and face value of 5 will be 5. All number face value will be same.

2):-Place value of a digit:-In a given number place value of a number will be depend on its place.

Example:-2615 find the place value of 6.

Solution:-place value of 6 will be 600 we count place value  from the unit digit.

Place value of 5=5*1=5

Place value of 1=1*1=10

Place value of 6=6*100=600

Place value of 2=2*1000=2000

Type of Numbers:-

1):-Natural numbers worksheet:-Which numbers are used for counting they called natural numbers.

Example:-1,2,3,4,5,6…………………

2):-Whole numbers Definiation:-When we added 0 in natural numbers they called whole numbers on other hand we can say that whole numbers are started from 0 and all natural numbers are whole numbers.

Example:- 0,1,2,3,4,5,6…………….

3):-Integers :-When we count numbers –

They called integers. Integers are tree types.

1)Negative integers      2)zero   3)positive integers

-∞……..-5 -4  -3  -2 -1  0 +1 +2 +3 +4 +5……+∞

Descending order      0     Ascending order

When we move 0 to right side number will be increasing order and when we move 0 to left  side numbers will be descending order.

4):- Rational numbers:- When we can show any number in p/q form and q≠0 then its called rational number.

Example:-1/2, 2/3, 3/5, 4…..

5):- irrational number:- When we can’t show any number in p/q form its called irrational number.

Example:-

6):-  Which numbers are divided by 2 are called even number.

Example:-2,4,6,70,……

7):-Odd numbers:– which numbers are not divided by 2 are called odd numbers.

Example:- 3,5,7,9……

8):- Prime numbers:– Which numbers are divided by self  and only 1 are called prime numbers.

Example:- 2, 3, 5, 7…..

Sum of first n positive integers= n(n+1)/2

Sum of first n positive numbers square= n(n+1)(2n+1)/6

Sum of the  first n positive numbers cube =[n(n+1)/2]²

Sum of first n even numbers =n(n+1)

Sum of first n odd numbers =n²

Example:- How many odd numbers are 11 to 30.

Solution:- 11, 13, 17, 19, 23, 29

Example:- What is the sum of 1+2+3……..20.

Solution:- we use here n(n+1)/2

Where n=20

So; 20(20+1)/2=10*21=210

Example:- find the sum of all odd numbers between 10 to 26.

Solution:- sum of odd numbers =n²

So number of odd numbers between 10 to 26 are 8.

So n==8  then sum of its =8²=64

 

Number System Exercise