**Magic of Numbers **

**Magical 1**

3 x 37 = 111

33 x 3367 = 111,111

333 x 333667 = 111,111,111

3333 x 33336667= 111,111,111,111

33333 x 3333366667= 111,111,111,111,111

333333 x 333333666667 = 111,111,111,111,111,111

Consider the L.H.S of the above numbers. The number of 3s in both the numbers are same and 6 is one less than the number of 3 and there is only one 7. Then in the final product, N would appear three times the number of threes in the first number on the LHS.

**6 when multiplied with 7 give 4 and 2 **

6 x 7 = 42

66 x67 = 4422

666 x 667 = 444222

6666 x 6667 = 44442222

**For multiplication such as the above:**

The number of digits in both the numbers is same, the 2^{nd} number has one 6 less than the number of 6’s the 1^{st} number has .

The number of 4’s and 2’s is equal to the number of 6’s in the 1^{st} number

**Cyclic numbers **

142857 is called as the cyclic number, since its digits are rotated around when multiplied by any number from 1 to 6

142857 x 1 = 142857

142857 x 5= 714285

142857 x 4= 571428

142857 x 6 = 857142

142857 x 2= 285714

142867 x 3 = 428571

The same method helps us calculating fractions involving 7 in denominator

We know 1/7 = 0.142857

Thus 2/7 will be a value close to 0.28 and directly we will write exact answer as numbers repeat in cyclic order as shown in diagram. Hence exact answer will be 0.285714

Similarly 3/7 will be a value close to 0.42 and directly we will write exact answer as numbers repeat in cyclic orderas shown in diagram. Hence exact answer will be 0.428571

Similarly 4/7 will be a value close to 0.56 and directly we will write exact answer as numbers repeat in cyclic orderas shown in diagram. Hence exact answer will be 0.571428

Similarly 5/7 will be a value close to 0.7 and directly we will write exact answer as numbers repeat in cyclic orderas shown in diagram. Hence exact answer will be 0.714285

Similarly 6/7 will be a value close to 0.84 and directly we will write exact answer as numbers repeat in cyclic orderas shown in diagram. Hence exact answer will be 0.857142

awesome and interesting tricks.. good work..

good