算式1×1+11×11+111×111+……111…111×111…111(2010个1)的结果的末三位数字是 。

2024-12-01 01:46:13
推荐回答(5个)
回答1:

这个题看似很难,其实是在找规律。1×1=1 11×11=121 111×111=12321 1111×1111=1234321 11111×11111=123454321 。。。。。。。。。
规律找到了得数为1,121,12321,1234321,123454321,12345654321,。。。。。
观察个位都是1,一共2010个,
所以有以上可得个位是1×2010=2010 个位即为0,进位201个十,
观察十位,除了第一个数都是2
所以十位是(2010-1)×2=4018 加上个位进的201 得4219 所以十位为9 进位421个百
观察百位,除了前两个数都是3
所以百位是(2010-2)×3=6024 加上十位进的421 得6445 所以百位为5 进位644个千
以后的位数照这个规律都可以算出来。
嗯呵呵,所以答案一幕了然,即为590
我在犹豫我是否帮了倒忙。希望这位同学以后掌握规律的返璞归真!

回答2:

如果题目要求是说算式本身包含2010个1的话,那么此题无解,算式本身就不成立。

回答3:

首先看最后一位数,不管是1×1 或11×11 还是 111×111……末位都是1(可以试试嘛)同样的道理,也就是有2010个1相加,所以最后和的末位应该是0,同时向前一位进位201,不管是11×11 还是 111×111……倒数第二位都是2,总共加起来就有2009个2,再加上最末位进上来的201,就是4219,所以倒数第二位是9,同时向第三位进421,;求第三位的方法类似,应该是5,所以末三位应该是590

回答4:

590

回答5:

一楼厉害

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