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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