Question

（2013?乐清市模拟）计算
（0.1+0.12+0.123+0.1234）×（0.12+0.123+0.1234+0.12345）-（0.1+0.12+0.123+0.1234+0.12345）×（0.12+0.123+0.1234）

Answer 1

分析：通过观察，此题中每个括号内的数字很接近，于是可设（0.1+0.12+0.123+0.1234）=A，（0.12+0.123+0.1234）=B，然后运用代入求值，解决问题．

解答：解：设（0.1+0.12+0.123+0.1234）=A，（0.12+0.123+0.1234）=B，则A-B=0.1，
（0.1+0.12+0.123+0.1234）×（0.12+0.123+0.1234+0.12345）-（0.1+0.12+0.123+0.1234+0.12345）×（0.12+0.123+0.1234）
=A×（B+0.12345）-（A+0.12345）×B
=AB+0.12345A-（AB+0.12345B）
=AB+0.12345A-AB-0.12345B
=0.12345×（A-B）
=0.12345×0.1
=0.012345．

点评：对于此类问题，一般采取把某个算式用字母代替，然后把字母代入算式中，使运算简便．