Eiitz..., do not worry because here I am not asking you to bother counting the numbers. But, the unique facts figures 6 and 9 this will make you feel that mathematics is interesting. Please read, observe and then comment.
Unique Facts Numerals 6 and 9-We would be familiar with arithmetic operations (like + , -, *, and /). It turned out that those numbers have the uniqueness that we might not know.
Here we will discuss the uniqueness of the number 6 and number 9 are extracted from various sources:
Numbers 666... 666
The uniqueness of number 6 :
1 + 2 + 3 + 4 + 5 + 6 = 21
1 + 2 + 3 + .......+ 66 = 2211
1 + 2 + 3 + .......+ 666 = 222111
1 + 2 + 3 + .......+ 6666 = 22221111
1 + 2 + 3 + .......+ 66666 = 2222211111
1 + 2 + 3 + .......+ 666666 = 222222111111
Now try to illustrate the answer to these questions.
1 + 2 + 3 + ...+ n = 222...222111...111 (number 2 and 1 respectively was the 2009 digits)
Determine the value of n
In mathematics, there are some unique facts of the number 666:
* is a palindrome number ( symmetric ): 666
* Represents the sum of 62 = 36 the first number, ie 1+2+3+4..….+35+36 =666
* The total number of prime numbers up to 666 is 121. numbers which is the square of 11.
* 6=(32) − (22) + 1
* 66=(34) − (24) + 1
* 666=(36) − (26) + 1
* The total of the amount of the first seven prime numbers square, ie : 22 + 32 + 52 + 72 + 112 + 132 + 172 = 666
* In Roman numerals, 666 represented as DCLXVI (D = 500, C = 100, L = 50, X = 10, V = 5, I = 1). DIC LVX is a representation of dicit lux. Dicit lux later known as the voice of light.
What about the number 9?, evidently, confidential and unique facts of the number nine is very much, following its derived.
Try search results of 63 x 99.
How do we solve it?
One way to calculate 63 x 99 is by multiplying the composite. However, there are other ways to calculate the product of these two numbers :
Because 99 = 100 - 1,
So, 63 x 99 = 63 ( 100 - 1 )
= 63. 100 - 63. 1
= 6300 - 63
= 6237
For multiplying 999 x 27, can be solved with the following way:
Because 999 = 1000 - 1
then 999 x 27 = (1000 - 1) x 27
= 2700 - 27
= 26.973
Furthermore, how is the result of, eg 52 x 999 ? Try to do with technique as before.
If the description, examples and questions above have been interpreted, then we will exploit the other uniqueness of the 9.
In integer division by the number 9, there are things that are very unique. Let us consider an example.
Example 1:
If 12 divided by 9, then the result is 1 and the remaining is 3.
If the figures at 12, namely 1 and 2 summed, then the result is 1 + 2 = 3 (the residual of the division by 9).
Example 2:
If 78 divided by 9, then the result is 8 and the remainder is 6.
If the numbers in 78, namely 7 and 8 are added, then the result is 7 + 8 = 15. Furthermore, if the figures at 15, namely 1 and 5 are added, then the result is 1 + 5 = 6 (residual of the division by 9).
Example 3:
If 878 is divided by 9, then the result is 97 and the remainder is 5.
If the numbers on the 878, ie 8, 7 and 8 are added together then the result is 8 7 8 = 23. Furthermore, if the numbers at 23, ie 2 and 3 added, then the result is 2 3 = 5 (sisa pembagian oleh 9).
From the examples above can be concluded“ Every integer is divided by 9, maka sisanya adalah jumlah berulang dari angka-angka yang terdapat pada bilangan yang dibagi itu sampai memperoleh sebuah bilangan 0 sampai 8 “.
the remainder is the number of recurrent figures contained in the number of divided it up to obtain a number from 0 to 8 ".
Another interesting of the number 9, You can see the following row:
12345679 x 9 = 111.111.111
12345679 x 18 = 222.222.222
12345679 x 27 = 333.333.333
12345679 x 36 = 444.444.444
12345679 x 45 = 555.555.555
12345679 x 54 = 666.666.666
12345679 x 63 = 777.777.777
12345679 x 72 = 888.888.888
12345679 x 81 = 999.999.999
Daftar hasil kali bilangan 987654321 dengan sembilan bilangan asli kelipatan 9 yang pertama tampak seperti berikut :
987654321 x 9 = 8.888.888.889
987654321 x 18 = 17.777.777.778
987654321 x 27 = 26.666.666.667
987654321 x 36 = 35.555.555.556
987654321 x 45 = 44.444.444.445
987654321 x 54 = 53.333.333.334
987654321 x 63 = 62.222.222.223
987654321 x 72 = 71.111.111.112
987654321 x 81 = 80.000.000.001
Here are the results of the uniqueness of 9.
1 x 9 + 2 = 11
12 x 9 + 3 = 111
123 x 9 + 4 = 1111
1234 x 9 + 5 = 11111
12345 x 9 + 6 = 111111
123456 x 9 + 7 = 1111111
1234567 x 9 + 8 = 11111111
12345678 x 9 + 9 = 111111111
It also Unique Fact of Numeral 9 :
9 x 9 + 7 = 88
98 x 9 + 6 = 888
987 x 9 + 5 = 8888
9876 x 9 + 4 = 88888
98765 x 9 + 3 = 888888
987654 x 9 + 2 = 8888888
9876543 x 9 + 1 = 88888888
98765432 x 9 + 0 = 888888888
I. UNIQUE FACTS NUMBER 9
0 x 9 + 0 = 0
1 x 9 + 1 = 10
12 x 9 + 2 = 110
123 x 9 + 3 = 1110
1234 x 9 + 4 = 11110
12345 x 9 + 5 = 111110
123456 x 9 + 6 = 1111110
1234567 x 9 + 7 = 11111110
12345678 x 9 + 8 = 111111110
123456789 x 9 + 9 = 1111111110
II. UNIQUE FACTS FIGURES 9
1 x 1 = 1
11 x 11 = 121
111 x 111 = 12321
1111 x 1111 = 1234321
11111 x 11111 = 123454321
111111 x 111111 = 12345654321
1111111 x 1111111 = 1234567654321
11111111 x 11111111 = 123456787654321
111111111 x 111111111 = 12345678987654321
III. UNIQUE FACTS FIGURES
1 x 8 + 1 = 9
12 x 8 + 2 = 98
123 x 8 + 3 = 987
1234 x 8 + 4 = 9876
12345 x 8 + 5 = 98765
123456 x 8 + 6 = 987654
1234567 x 8 + 7 = 9876543
12345678 x 8 + 8 = 98765432
123456789 x 8 + 9 = 987654321
IV. UNIQUE FACTS FIGURES 9
1 x 18 + 1 = 19
12 x 18 + 2 = 218
123 x 18 + 3 = 2217
1234 x 18 + 4 = 22216
12345 x 18 + 5 = 222215
123456 x 18 + 6 = 2222214
1234567 x 18 + 7 = 22222213
12345678 x 18 + 8 = 222222212
123456789 x 18 + 9 = 2222222211
V. UNIQUE FACTS NUMERAL 9
123456789 + 987654321 = 1111111110
1 x 142857 = 142857 (same numbers)
2 x 142857 = 285714 (same numbers, different order )
3 x 142857 = 428571 (same numbers, different order)
4 x 142857 = 571428 (same numbers, different order )
5 x 142857 = 714285 (same numbers, different order)
6 x 142857 = 857142 (same numbers, different order)
7 x 142857 = 999999 (fantastic result!)
VI. UNIQUE FACTS FIGURES 9
Any number can be multiplied by 9, then results numbers are summed, then the result = 9. Let us prove.
1 x 9 = 9
2 x 9 = 18, result of 1 + 8 = 9
3 x 9 = 27, result of 2 + 7 = 9
4 x 9 = 36, result of 3 + 6 = 9
5 x 9 = 45, result of 4 + 5 = 9
6 x 9 = 54, result of 5 + 4 = 9
7 x 9 = 63, result of 6 + 3 = 9
8 x 9 = 72, result of 7 + 2 = 9
9 x 9 = 81, result of 8 + 1 = 9
10 x 9 = 90, result of 9 + 0 = 9, and so on., till infinity.
Another unique of nine.
22 x 9 = 198,
the fast way is 2 x 9 = 18, then insert number 9 in the middle, become 198.
33 x 9 = 297
44 x 9 = 396
55 x 9 = 495
66 x 9 = 594
77 x 9 = 693
88 x 9 = 792
99 x 9 = 891
UNIQUE FACTS FIGURES NINE-If the 3-digit twin numbers, then insert number 99 in the middle. Let's prove it!
222 x 9 = 1998, fast way: 2 x 9 = 18, insert 99 in the middle.
333 x 9 = 2997
444 x 9 = 3996
555 x 9 = 4995
How...? Is not it unique?... Math can be fun... Please tell your friends about UNIQUE FACTS OF SIX AND NINE.
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