#### Answer

$$8.52\times 10^{2}$$

#### Work Step by Step

Rearrange factors and multiply
$$(4.237\times 10^{4})(2.01\times 10^{-2})=(4.237\times 2.01)(10^{4}\times 10^{-2})=8.51637\times 10^{2}$$
In scientific notation, the number of significant digits is the number of digits in the leading number between $1$ and $10$. The final answer should have the same number of significant digits as the least number of significant digits in any of the numbers involved in the multiplication.
$4.237\times 10^{4}$ has $4$ significant digits
$2.01\times 10^{-2}$ has $3$ significant digits
In this case the number of significant digits in the final answer should be $3$ so round to :
$$8.52\times 10^{2}.$$