Question

乘积 $4^5 \cdot 5^{10}$ 有多少位数字？

How many digits are in the product $4^5 \cdot 5^{10}?$

$8$

$9$

$10$

$11$

$15$

知识点：指数数字

为了求位数，可以尝试把这个数写成 $10$ 的幂。

有 $\begin{align*} 4^5 \cdot 5^{10} &= 2^{10} \cdot 5^{10} \\ &= 10^{10}. \end{align*}$

这说明所求数是 $1$ 后面跟着 $10$ 个零，共有 $11$ 位数字。

所以正确答案是 D。

To find the number of digits, we can try to express this number in terms of powers of $10.$

We get that $\begin{align*} 4^5 \cdot 5^{10} &= 2^{10} \cdot 5^{10} \\ &= 10^{10}. \end{align*}$

This shows that the desired number is $1$ followed by $10$ zeros, for a total of $11$ digits.

Thus, D is the correct answer.