Question

当 $10^{93} - 93$ 写成一个整数时，它的各位数字之和是多少？

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

$10$

$93$

$819$

$826$

$833$

知识点：位值数字

$10^{93}$ 是 $1$ 后面跟着 $93$ 个零；减去 $93$ 只会改变右端

$10^{93}$ is a $1$ followed by $93$ zeros; subtracting $93$ changes only the right end

结果是一串九，最后以 $07$ 结尾；确定有多少个九

The result is a block of nines ending in $07;$ determine how many nines there are

从 $10^{93}$ （ $1$ 后面跟 $93$ 个零）减去 $93$ ，结果为 $91$ 个九后接 $07$ 。

数字和为 $91 \times 9 + 0 + 7 = 819 + 7 = 826$ 。

所以正确答案是 D。

Subtracting $93$ from $10^{93}$ (a $1$ followed by $93$ zeros) gives a number that is $91$ nines followed by $07.$

The digit sum is $91 \times 9 + 0 + 7 = 819 + 7 = 826.$

Thus, the correct answer is D .