Question

（2013?樂清市模擬）計算
（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：通過觀察，此題中每個括號內(nèi)的數(shù)字很接近，于是可設(shè)（0.1+0.12+0.123+0.1234）=A，（0.12+0.123+0.1234）=B，然后運用代入求值，解決問題．

解答：解：設(shè)（0.1+0.12+0.123+0.1234）=A，（0.12+0.123+0.1234）=B，則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．

點評：對于此類問題，一般采取把某個算式用字母代替，然后把字母代入算式中，使運算簡便．