Skip to main content

Number System ( Basics )

NUMBER SYSTEM



TYPES OF NUMBERS

1. Natural Numbers: Numbers starting from 1, 2, 3, .......... are Natural Numbers.

2. Whole Numbers : Numbers starting from 0, 1, 2, 3, .......... are Whole Numbers. 

3. Integers : Negative, Zero and Positive Numbers comes in category of Intergers. 

     Ex. : -3, -2, -1, 0, 1, 2, 3, etc.

4. Negative Numbers : Numbers like -1, -2, -3, -4 ......... are Negative numbers

5. Positive Numbers : Numbers like 1, 2, 3, 4, .....are Positive Numbers.

6. Rational Numbers : Numbers that are being expressed in the form of p/q.

7. Irrational Numbers : An infinite Non-Recurring , Non - Terminating Decimal Number . Such numbers can't be expressed in the form of p/q.

8. Even Numbers : Numbers that are divisible by 2.

9. Odd Numbers : Numbers that can't be divisible by 2.

10. Prime Numbers : Numbers that are divisible by 1 or itself.   

 NOTE : 2 is only even prime number.
              There are 25 prime numbers upto 100. (2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89 and 97)

11. Co- Prime Numbers : Pair of numbers are considered to be prime if their H. C. F. is 1. 

       Ex.:  5 and 12 are co - prime to each other.
             Consecutive Numbers are co-prime pairs.
             All prime numbers are co-prime pairs.

12. Composite Numbers : Numbers having factors other than itself and 1.

       NOTE : 1 is neither a composite number nor a prime number.

13. Real Numbers : Natural Numbers, Integers, Whole Numbers, Rational Numbers and Irrational Numbers constitutes set of Real Numbers. 

14. Perfect Numbers :  If sum of all the factors of a number excluding itself is equal to the number 

      Ex.:  6 is the first perfect number.  (1 + 2+3)
       Next three perfect Numbers are 28, 496, and 8128

Comments

Post a Comment

Popular posts from this blog

HCF and LCM

HCF and LCM FACTORS / DIVISORS = Numbers that divide any number completely, without leaving any Remainder are its factors. Example : Factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.                    Factors of 90 are 1, ,2, 3, 5 , 6, 9, 10, 15, 18, 30, 45, 90 MULTIPLES =   Numbers that fall in tables of any given number are its Multiples. Examples  : Multiples of 12 are 12, 24, 36, 48, 60, 72, 84, 96……                       Multiples of 5 are 5, 10, 15, 20, 25, 30, 35, 40, 45, 50 ….. HIGHEST COMMON FACTOR (H.C.F.) /  GREATEST COMMON DIVISOR (G.C.D.) =   Largest number that divides two or more than two given numbers. Examples : Calculate the  H.C.F. of 45 and 27  Sol : Factors of 45 = 1, 3, 5, 9, 15, 45       ...
Post a Comment
Read more

Digital Sum Balance (D.S.)

A single digit is obtained by adding all the digits of a number is called Digital Sum Balance (D.S.)   Ex :  12 → 1 + 2 → 3 24 → 2 + 4 → 6 21 → 2 + 1  → 3 9876 → 9 + 8 + 7 + 6 → 30 → 3 + 0 → 3 3452 → 3 + 4 + 5 + 2 → 14 → 1 + 4 → 5 Or,  On Dividing the digits by 9, the obtained Remainder is Digital Sum Balance.  Ex :    12    ━━ = 3                9      24 ━━━ = 6      9    3452 ━━━━ =  5      9 KEY HIGHLIGHTS : The range of D.S. always falls from 0 to 9. When we add 9 to a number, its Digital Sum will not change therefore in order to calculate Digital Sum we need to cancel out  all the 9’s.  9 + 1 → 10 → 1 9 + 2 → 11 → 2 9 + 3 → 12 → 3 9 + 4 → 13 → 4 9 + 5 → 14 → 5 9 + 6 → 15 → 6 9 + 7 → 16 → 7 9 + 8 → 17 → 8 9 + 9 → 18 → 9 Example : 123 45 → 6 → Digital Sum ...
Post a Comment
Read more

CLOCKS (ANGLE)

ANGLES A clock is composed of 360 ° with 12 equal divisions. (i.e. 60 Minutes) The angle between any two consecutive divisions = (360°)/12= 30° or 1 Min = 6 °A Angular value of a minute = (30°)/5= 6° Speed of the hands Each needle of a clock covers the angle of 30 °  to go from one division to the next, but it takes different times to cover this distance. Speed of a second hand = 360° per minute.  Speed of a minute hand = 6° per minute. Speed of an hour hand =1/2 ° per minute.  Example : Q 1. How much degree is covered by minute and hour hand between 02 :00 p.m. to 04 : 00 ? 120 ° and 180 ° 60 ° and 120 ° 120 ° and 60°  60 ° and 720 ° Sol : Between 02: 00 to 04 : 00 = 120 minutes. Distance covered by Hour hand =   120 * ½ = 60 °  Minute hand = 120 * 6 ° = 720 ° = 2 rounds of the clock Q 2.  How much degree is covered by  hour hand between 12 noon to 03 : 45 p.m. ? 112.5 ° 150 ° 90 ° None of these Sol :  Between 12: 00 to 03 : 45 = 3 hours...
Post a Comment
Read more