We know number nine is a magical number. Sum of digit of all numbers , whose factor is nine, will be always be nine or multiple of nine. But is it the sole property of number nine only? Let’s investigate.

The number we use for our daily life is called decimal number. It is called decimal because we have ten digits for this number system, i.e 0,1,2,3,4,5,6,7,8,9. But we have other number systems also, for example, binary number system which comprises only 0 and 1 and octal system which comprises, 0,1,2,3,4,5,6, and 7 only. So the numbers in octal system will look like

1,2,3,4,5,6,7,10

11,12,13,14,15,16,17,20

21,22,23,24,25,26,27,30

31,32,33,34,35,36,37 etc.

Number 8,9, 18,19 is not written because 8 and nine do not exist in this number system.

And if you see, you can see 14

^{th }**number is 16 and 21**_{ }^{st}number is 25 in this list.So, 7 x 2 will be 16 and 6 + 1 = 7

Similarly, 7 x 3 will be 25 as 21

^{st}number in this list is 25 and 2 + 5 is 7.Also, look at this

Decimal | Octal |

9x2 = 18 | 7x2=16 |

9x3=27 | 7x3=25 |

9x4=36 | 7x4=34 |

9x5=45 | 7x5=43 |

9x6=54 | 7x6=52 |

In both number system, the products have digits are in increasing order for first digit and in decreasing order for second digit.

A number system with nine will look like this

1,2,3,4,5,6,7,8,10

11,12,13,14,15,16,17,18,20

21,22,23,24,25,26,27,28,30

**And so on**

And we can see

8x2=17

8x3=26 and so on. So, all properties are transferred to number eight.

Can you try for some other number system? What was your observations? Please write in comment.

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