数学乘法巧算,急99.9(2003个“9”)*99.9(2003个“9”)+199.9(2003个“9”),结尾有多少个“0”?
问题描述:
数学乘法巧算,急
99.9(2003个“9”)*99.9(2003个“9”)+199.9(2003个“9”),结尾有多少个“0”?
答
99......9(2003个9)*99......9(2003个9)+199.....9(2003个9)
=99......9(2003个9)*99......9(2003个9)+99.....9(2003个9)+100……0(2003个0)
=99……9(2003个9)*(99……9(2003个9)+1)+100……0(2003个0)
=99……900……0(2003个0)+100……0(2003个0)
=100……0(4006个0)
答
原式=
(100...00(2003个0) -1)*999..99(2003个9) + 1999...9(2003个9)
=999...900..00(2003个9,2003个0)-999..9(2003个9)+1999..9(2003个9)
=999...900..00(2003个9,2003个0 + 1000..0(2003个0)
所以有2003个0