기출문제/수학

숫자 1, 111111111 x 111111111 = 12345678987654321

Jobs9 2024. 11. 19. 11:20
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숫자 1의 비밀
 

111111111 x 111111111 = 12345678987654321?

Because 111111111 times 111111111 equals 12345678987654321 according to the laws of multiplication for real numbers.

If your question is more along the lines of “Why is there such a nice pattern in this product,” then perhaps I can elaborate a bit further. 
Note that 111111111 = 100000000 + 10000000 + … + 100 + 10 + 1. As a consequence of the distributive property of multiplication over addition, 

111111111×111111111=111111111×(100000000+10000000+ +100+10+1) =11111111100000000+1111111110000000++11111111100+1111111110+111111111. 




1x1=1

11x11=121

111x111=12321

1111x1111=1234321

11111x11111=123454321

111111x111111=12345654321

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