1991 AMC 8 第 1 题

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所有题目均经美国数学协会(MAA)官方合法授权使用。

1.

下列表达式的值是多少? 1,000,000,000,000777,777,777,777? \begin{aligned} &1{,}000{,}000{,}000{,}000 \\ &\quad {}- 777{,}777{,}777{,}777? \end{aligned}

What is the value of 1,000,000,000,000777,777,777,777? \begin{aligned} &1{,}000{,}000{,}000{,}000 \\ &\quad {}- 777{,}777{,}777{,}777? \end{aligned}

222,222,222,222222{,}222{,}222{,}222

222,222,222,223222{,}222{,}222{,}223

233,333,333,333233{,}333{,}333{,}333

322,222,222,223322{,}222{,}222{,}223

333,333,333,333333{,}333{,}333{,}333

答案:B
知识点:位值
难度评级:450
解答:

竖式相减得 1,000,000,000,000777,777,777,777=222,222,222,223. \begin{aligned} &1{,}000{,}000{,}000{,}000 \\ &\quad {}- 777{,}777{,}777{,}777 \\ &= 222{,}222{,}222{,}223. \end{aligned}

也可以想成:从 777,777,777,777777{,}777{,}777{,}777 增加到 1,000,000,000,0001{,}000{,}000{,}000{,}000,个位要加 33,其余十一位各加 22

所以正确答案是 B

Lining up the subtraction gives 1,000,000,000,000777,777,777,777=222,222,222,223. \begin{aligned} &1{,}000{,}000{,}000{,}000 \\ &\quad {}- 777{,}777{,}777{,}777 \\ &= 222{,}222{,}222{,}223. \end{aligned}

Equivalently, to climb from 777,777,777,777777{,}777{,}777{,}777 up to 1,000,000,000,0001{,}000{,}000{,}000{,}000 you add 33 in the units place and 22 in each of the other eleven places.

Thus, the correct answer is B .

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