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1. 计算下面各题。
(1) $4.2×5 + 40.02×5 + 400.002×5 + 4000.0002×5 + 40000.00002×5$
(2) $(1.5 + 2.5 + \dots + 2026.5)×(2.5 + 3.5 + \dots + 2027.5) - (1.5 + 2.5 + \dots + 2027.5)×(2.5 + 3.5 + \dots + 2026.5)$
(1) $4.2×5 + 40.02×5 + 400.002×5 + 4000.0002×5 + 40000.00002×5$
(2) $(1.5 + 2.5 + \dots + 2026.5)×(2.5 + 3.5 + \dots + 2027.5) - (1.5 + 2.5 + \dots + 2027.5)×(2.5 + 3.5 + \dots + 2026.5)$
答案
(1) 222221.1111
(2) 3041.25
(2) 3041.25
2. 用两种方法计算:$\underbrace{888···8}_{2026个8}.8 × \underbrace{999···9}_{2026个9}.9$。
答案
方法一：
$\underbrace{888···8.8}_{2026个8}×\underbrace{999···9.9}_{2026个9}$
$=\underbrace{888···8.8}_{2026个8}×(\underbrace{1000···0}_{2026个0}-0.1)$
$=\underbrace{888···8}_{2027个8}\underbrace{000···0}_{2025个0}-\underbrace{888···8.88}_{2025个8}$
$=\underbrace{888···87}_{2026个8}\underbrace{111···1.12}_{2025个1}$
方法二：
0.8×0.9=0.72
8.8×9.9=87.12
88.8×99.9=8871.12
所以$\underbrace{888···8.8}_{n个8}×\underbrace{999···9.9}_{n个9}=\underbrace{888···87}_{n个8}\underbrace{111···1.12}_{(n-1)个1}$
因此，原式=$\underbrace{888···87}_{2026个8}\underbrace{111···1.12}_{2025个1}$
$\underbrace{888···8.8}_{2026个8}×\underbrace{999···9.9}_{2026个9}$
$=\underbrace{888···8.8}_{2026个8}×(\underbrace{1000···0}_{2026个0}-0.1)$
$=\underbrace{888···8}_{2027个8}\underbrace{000···0}_{2025个0}-\underbrace{888···8.88}_{2025个8}$
$=\underbrace{888···87}_{2026个8}\underbrace{111···1.12}_{2025个1}$
方法二：
0.8×0.9=0.72
8.8×9.9=87.12
88.8×99.9=8871.12
所以$\underbrace{888···8.8}_{n个8}×\underbrace{999···9.9}_{n个9}=\underbrace{888···87}_{n个8}\underbrace{111···1.12}_{(n-1)个1}$
因此，原式=$\underbrace{888···87}_{2026个8}\underbrace{111···1.12}_{2025个1}$
