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 2nd number has one 6 less than the number of 6’s the 1st number has .
The number of 4’s and 2’s is equal to the number of 6’s in the 1st 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
