999.99×999.99+199.99999.99(9有1992个)×999.99(9有1992个)×+199.99(9有1992个)

问题描述:

999.99×999.99+199.99
999.99(9有1992个)×999.99(9有1992个)×+199.99(9有1992个)

∵999......99(9有1992个)×999......99(9有1992个)+199......99(9有1992个)
∴999......99×999......99+199......99
=(10^1992-1)^2+(10^1992+10^1992-1)
=(10^1992-1)^2+(2×10^1992-1)
设10^1992=t,则
原式=(t-1)^2+2t-1
=t^2
=(10^1992)^2
=10^(1992×2)
=10^3984

1000……002 (共有3983个0)

999......99×999......99+199......99
=(1000……00-1)×(1000……00-1)+199……99 (分别是1992个0)
=1000……000 - 999……99 - 999……99 + 1 + 199……99
(0有3984个,9分别都是1992个)
=1000……002 (共有3983个0)

999.99×999.99+1999.99=(1999...99-1000...00)×999...99+1999...99=1999...99×999...99-1000...00×999...99 +1999...99=1999...99×(999...99+1)-1000...00×999...99=1999...99×1000...00-1000...00×999......