AMC8 1993

AMC8 1993 · Q20

AMC8 1993 · Q20. It mainly tests Fractions, Base representation.

When $10^{93} - 93$ is expressed as a single whole number, the sum of the digits is

当$10^{93} - 93$表示为单个整数时，其各位数字之和是

(A) 10 10

(B) 93 93

(D) 826 826

(E) 833 833

Answer

Correct choice: (D)

正确答案：（D）

Solution

Since $10^{93}=1\underbrace{00\cdots00}_{93\text{ zeros}}$, we have \[10^{93}-93=\underbrace{99\cdots9}_{91\text{ nines}}07.\] Thus the sum of the digits is $(91\times9)+7=826$.

因为 $10^{93}=1\underbrace{00\cdots00}_{93\text{ 个零}}$，所以 \[10^{93}-93=\underbrace{99\cdots9}_{91\text{ 个 9}}07.\] 因此各位数字之和为 $(91\times9)+7=826$。

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