திருவண்ணாமலை

கடவுளை வணங்கி நல்ல வாழ்க்கை வாழச் சொல்வது சமயம்.

கடவுளை வணங்குவது எப்படி என்று சமயம் சொல்லும்.

நல்ல வாழ்க்கை வாழ்வது எப்படி என்றும் சமயம் சொல்லும்.

நல்ல நினைப்பும் நல்ல பேச்சும் நல்ல செயலும் நல்ல வாழ்க்கைக்கு அடிப்படை.

இவற்றைப் புண்ணியம் என்பார்கள் சான்றோர்கள்.

தீய நினைப்பும் தீய பேச்சும் தீய செயலும் வாழ்க்கையைக் கெடுத்துவிடும்.

இவற்றைப் பாவம் என்பார்கள் சான்றோர்கள்.

புண்ணியம் நமக்கு நன்மை தரும்.

பாவம் நமக்குத் தீமை தரும்.

புண்ணியம் செய்யத் தூண்டுவது கடவுள் நெறி.

பாவம் செய்யாமல் இருக்க உதவுவது கடவுள் நெறி.

கடவுள் நெறியே சமய நெறி.

கங்கை யாடிலென் காவிரி யாடிலென்
கொங்கு தண்கும ரித்துறை யாடிலென்
ஓங்கு மாகட லோதநீ ராடிலென்
எங்கும் ஈசன் எனாதவர்க் கில்லையே.

Names for Powers of 10

Names for Powers of 10

Values Zero's Names 100 0 One 101 1 Ten 102 2 Hundred 103 3 Thousand 104 4 Myriad 106 6 Million 109 9 Billion 1012 12 Trillion 1015 15 Quadrillion 1018 18 Quintillion 1021 21 Sextillion 1024 24 Septillion 1027 27 Octillion 1030 30 Nonillion 1033 33 Decillion 1036 36 Undecillion 1039 39 Duodecillion 1042 42 Tredecillion 1045 45 Quattuordecillion 1048 48 Quindecillion 1051 51 Sexdecillion 1054 54 Septdecillion / Septendecillion 1057 57 Octodecillion 1060 60 Nondecillion / Novemdecillion 1063 63 Vigintillion 1066 66 Unvigintillion 1069 69 Duovigintillion 1072 72 Trevigintillion 1075 75 Quattuorvigintillion 1078 78 Quinvigintillion 1081 81 Sexvigintillion 1084 84 Septenvigintillion 1087 87 Octovigintillion 1090 90 Novemvigintillionn 1093 93 Trigintillion 1096 96 Untrigintillion 1099 99 Duotrigintillion 10100 100 Googol 10102 102 Trestrigintillion 10120 120 Novemtrigintillion 10123 123 Quadragintillion 10138 138 Quinto-Quadragintillion 10153 153 Quinquagintillion 10180 180 Novemquinquagintillion 10183 183 Sexagintillion 10213 213 Septuagintillion 10240 240 Novemseptuagintillion 10243 243 Octogintillion 10261 261 Sexoctogintillion 10273 273 Nonagintillion 10300 300 Novemnonagintillion 10303 303 Centillion 10309 309 Duocentillion 10312 312 Trescentillion 10351 351 Centumsedecillion 10366 366 Primo-Vigesimo-Centillion 10402 402 Trestrigintacentillion 10603 603 Ducentillion 10624 624 Septenducentillion 10903 903 Trecentillion 102421 2421 Sexoctingentillion 103003 3003 Millillion 103000003 3000003 Milli-Millillion

Dividing by 5

Dividing by 5

Dividing a large number by five is actually very simple. All you do is multiply by 2 and move the decimal point:

195 / 5

Step1: 195 * 2 = 390
Step2: Move the decimal: 39.0 or just 39

2978 / 5

step 1: 2978 * 2 = 5956
Step2: 595.6

Square a 2 Digit Number Ending in 5

Square a 2 Digit Number Ending in 5

For this example we will use 25

* Take the "tens" part of the number (the 2 and add 1)=3
* Multiply the original "tens" part of the number by the new number (2x3)
* Take the result (2x3=6) and put 25 behind it. Result the answer 625.

Try a few more 75 squared ... = 7x8=56 ... put 25 behind it is 5625.
55 squared = 5x6=30 ... put 25 behind it ... is 3025.

The 11 Rule

The 11 Rule
You likely all know the 10 rule (to multiply by 10, just add a 0 behind the number) but do you know the 11 rule? It is as easy! You should be able to do this one in you head for any two digit number. Practice it on paper first!

To multiply any two digit number by 11:

* For this example we will use 54.
* Separate the two digits in you mind (5__4).
* Notice the hole between them!
* Add the 5 and the 4 together (5+4=9)
* Put the resulting 9 in the hole 594. That's it! 11 x 54=594

The only thing tricky to remember is that if the result of the addition is greater than 9, you only put the "ones" digit in the hole and carry the "tens" digit from the addition. For example 11 x 57 ... 5__7 ... 5+7=12 ... put the 2 in the hole and add the 1 from the 12 to the 5 in to get 6 for a result of 627 ... 11 x 57 = 627
Practice it on paper first!

Number Systems

• All counting numbers together with 0 are called whole numbers.


• 0 is the smallest whole number and there is no largest whole number.


• Our number system is based on counting in tens i.e. it has base 10.
  Every whole number can be written by using the symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 called digits.



• The place value of a (non-zero) digit depends upon the place it occupies in the number; the place value
  of the digit 0 is always 0 regardless of the place it occupies in the number.


• The face value of a digit in a number is the digit itself, regardless of the place it occupies
  in the number.


• Addition properties of whole numbers
  
  Closure property: If a and b are any whole numbers then a +b is also a whole number.
  
  Commutative property: If a and b are any whole numbers then a+b= b+a.
  
  
  Associative law: If a, b, c are any whole numbers then (a+b)+c = a+(b+c).
  


• Multiplication properties of whole numbers
  
  Closure property: If a and b are any whole numbers then a × b is also a whole number.
  
  Commutative property: If a and b are any whole numbers then a × b = b × a.
  
  
  Associative law: If a, b, c are any whole numbers then (a × b) × c = a × (b × c).
  
  Distributive law: If a, b, c are any whole numbers then a × (b+c)=a × b + a × c.
  


• Division algorithm
  
  If a is any whole number and b is another
  smaller non-zero whole number then there exist unique whole numbers q
  and r such that
  a = b × q + r where 0 r < b.

Multiply

Multiply 92 by 67
92
x 67
(Mentally) 2x7 is 14; write 4 carry 1;
9x7 +2x6 = 75 +carry 1 = 76; write 6, carry 7
9x6 is 54, add carry 7 to get 61 -so answer is 6164

Multiply 2376 by 4060
2376
x 4060
6x0 = 0; write 0;
7x0 +6x6 = 36; write 6 carry 3;
3x0 +7x6 +6x0 = 42 +carry 3 = 45; write 5 carry 4
2x0 +3x6 +7x0 +6x4 = 42 +carry 4 = 46; write 6 carry 4
2x6 +3x0 +7x4 = 40 +carry 4 = 44; write 4 carry 4
2x0 +3x4 = 12 +carry 4 = 16; write 6 carry 1
2x4 = 8 +carry 1 = 9; write 9. End. Answer is 9646560

Vertically and Crosswise

Multiple:
Question: Multiply 432 by 617.

Answer:

       432

    x 617

   3024

     432

 2592   

 266544



More the number of digits in the numbers, more lines and time you consume.
No more! Using the Sutra "Vertically and Crosswise", you have

Step 1 (mentally, don't write on notebook) : vertically (last digits) :

          2x7=14; write 4 carry 1

Step 2 (mentally) : crosswise (last two digits) :

          3x7 +2x1 = 23 +carry 1 = 24; write 4 carry 2

Step 3 : vertically and crosswise (three digits) :

           4x7 + 3x1 +2x6 = 43 +carry 2 = 45; write 5 carry 4

Step 4 : (move left; first two digits) :

        4x1+3x6 = 22 +carry 4 = 26; write 6 carry 2

Step 5 : (move left; first digit of each number) :

       4x6 = 24 +carry 2 = 26. End.

Write answer : 266544