初一数学题--用简便方法计算:99...9×99...9+99...9

解:
99....9×99....9+199.....9
=99....9*(1000....0-1)+(1000....0+999...9)
=999..90000000..0-9999...9+100000...0+999..9(加n个9..9减去n个999..9结果为0)
=999...9000000..0+10000...0
=100000...0(2n个0)

99...9×99...9+99...9=(99...9+1)*99...9=100...000*99...9=99...900...0
99...900...0 2005个9,2005个0

99...9×99...9+99...9
=99...9×(99...9+1)
=99...9×100...0
=99...900...0
2005个9 2005个0

原式=(99...9+1)*999...9=999....90000....000
即2005个9后有2005个0

99...900...0 共25个9 25个0

99...9×99...9+99...9
=99...9×（99..9+1）
＝99...9×10^2006