解:(1)200.9×10%+2.009×490+0.2009×5000,
=200.9×0.1+200.9×4.9+200.9×5,
=200.9×(0.1+4.9+5),
=200.9×10,
=2009;
(2)[
-(
-
)]×
,
=[
-
]×
,
=[
]×
,
=
,
=
;
(3)(
+
+
)×24,
=
24
24,
=10+6+9,
=25;
(4)
+
+
+
+
+
+
+
,
=(1
)+(
)+(
)+(
)+(
)+(
)+(
)+(
),
=1-
,
=
.
分析:(1)200.9×10%+2.009×490+0.2009×5000,首先根據(jù)積的變化規(guī)律,一個(gè)因數(shù)擴(kuò)大10倍、100倍…,另一個(gè)因數(shù)縮小10倍、100倍…,積不變,原式轉(zhuǎn)化為200.9×0.1+200.9×4.9+200.9×5,再應(yīng)用乘法分配律進(jìn)行簡算;
(2)[
-(
-
)]×
,根據(jù)分?jǐn)?shù)四則混合運(yùn)算的運(yùn)算順序,按照它們的計(jì)算法則直接進(jìn)行計(jì)算;
(3)(
+
+
)×24,應(yīng)用乘法分配律進(jìn)行簡算;
(4)
+
+
+
+
+
+
+
.根據(jù)分?jǐn)?shù)的拆分原理和方法,把每個(gè)分?jǐn)?shù)拆分成兩個(gè)單位分?jǐn)?shù)的差,相互抵消,這樣計(jì)算比較簡便.
點(diǎn)評:此題主要考查應(yīng)用整數(shù)的運(yùn)算定律和分?jǐn)?shù)的拆分方法,對分?jǐn)?shù)、小數(shù)四則混合運(yùn)算進(jìn)行簡便計(jì)算.