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题目要求我们计算1.45乘

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10的八次方乘上9.2乘10的负十二次方，再乘

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3.01乘10的负五次方

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然后使用小数和科学计数法

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写出答案

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所以这是1.45乘10的8次方再乘……

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我可以像这里这样再写出括号

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但是我要直接写成另一个乘号

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乘9.2乘10的负十二次方

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然后乘3.01乘10的负五次方

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也就是说，当我将这些括号连在一起写的时候

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其实我就是要将这个表达式

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乘以这个表达式

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再乘这个表达式

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然后因为所有的运算都是乘法

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那我做乘法的顺序就不重要了

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所以根据这个，我要更换这里的顺序

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这等于从这里来的1.45

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乘9.2乘3.01

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乘10的八次方……让我

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用紫色来写……乘10的八次方乘

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10的负十二次方乘10的负五次方

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那这很有帮助因为现在

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所有10的次方都在这里了

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我可以在它们两边加上括号

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然后所有不是10的次方都在这边

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这样我就能化简了

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假如说这边的底数都是10

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那我可以直接将次幂相加

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这等于10的8减12减5次方

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然后这些左手边的几项

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让我拿来计算器

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你也可以手算，这样快一点而已

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并且更没那么容易犯错

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1.45乘9.2乘3.01等于40.1534

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所以这等于40.1534

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当然，这还要乘10的

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这个次方

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然后我们简化一下这个次方

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就得到了40.1534乘10……8减12

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等于负4，减5等于负9

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10的负9次方

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现在你可能想说这已经是

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科学计数法了因为我这有一个数字

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乘10的某个次方

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但这还不太是科学计数法

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因为如果这个是科学计数法的话

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这里这个数必须是

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大于等于1并且小于10

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然后很明显，这个不小于10

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所以如果要用科学计数法

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这里是一个非零数字

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然后所有的小数

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都在这里

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所以这是要是一位非零数

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所以这是要是一位非零数

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很明显这里是两位数

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这个比10大

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你要这个比10小

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然后大于等于1

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所以最好的办法就是

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先把这里这部分用科学计数法表示

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这个就等于4.01534乘10

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你可以想这是从40到4

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要将这个小数点往左移

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将小数点往左移把40变成4

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就是除以了10

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所以你需要再乘回来一个10

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除以10再乘10

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另一种看法是

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4.0加上所有这些东西一起再乘10是40.1534

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所以4加上这些东西乘10

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的1次方，也就是10

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再乘这个——乘10的负9次方

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然后这个也是10的次方

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所以10的一次方乘10的负九次方

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就是10的负八次方

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然后我们还有这个4.01534乘10的负8次方

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现在我们用完科学计数法了

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题目要求我们用

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科学计数法和小数形式表达

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所以我们需要用小数形式表达

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也就是说把这个

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展开

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做这个的方法是，把所有数字都写出来

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所以我有4,0,1,5,3,4

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然后看着这个数

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我要从这个小数点开始

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现在，每当我除以一次10，或者说乘一次

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10的负一次方，我要将这个向左移一位

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所以10的负一次方——假如我乘

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10的负1次方，这就等于除以10

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所以我要将小数点向左移一位

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这里我要乘10的负8次方

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也就是说我要除以10的8次方

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所以我要将小数点向左移动

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八次

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记住这个的方法——看

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这是一个非常非常小的数字

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假如我乘这个，我应该得到一个更小的数字

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所以我应该将小数点往左移

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假如这是一个正8，那么

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这会是一个非常大的数字

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所以假如我乘一个10的非常大的次方

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我要将小数点向右移

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所以这整个应该

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比4.01534小

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我将小数点向左移动了8次

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第一次我将其移到了这里

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然后剩下的七次我只用往这里加0了

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所以1,2,3,4,5,6,7个0

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然后我会再小数点之前再加一个0这样更清楚

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然后我发现，假如你算上这个数

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那我总共有8个数

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我有7个0，然后算上这个是8

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再来一次，1,2,3,4,5,6,7,8

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做这个最好的方法是

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我从这个小数点开始

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我移动了1,2,3,4,5,6,7,

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8次

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这就是乘10的负8次方的效果

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然后我得到了这个数字

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当你看到像这样子的数字时

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你会开始理解为什么我们将一些数写成

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科学计数法

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这个占用的空间更小

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然后你立刻就知道这个数大概有多大

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这个更难写

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可能你会忘记一个0

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或者多加一个0

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然后读者需要坐下来一个个数有多少个0

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来确定这个大概多大或者

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多小

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总共有1,2,3,4,5,6,7个0

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再加上这个数

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这是我们怎么得到8的

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但这看着比科学计数法

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更加复杂