Answer
$$1.9\times 10^{-8}$$
Work Step by Step
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:
$3.972\times 10^{-5}$ has $4$ significant digits
$4.7\times 10^{-4}$ has $2$ significant digits
Therefore, the final answer should be rounded to have $2$ significant digits.
Rearrange factors and multiply:
$$(3.972\times 10^{-5})(4.7\times 10^{-4})=(3.972\times 4.7)(10^{-5}\times 10^{-4})$$
$$=1.9\times 10^{-8}.$$
