To determine how many times smaller $4 \times 10^{-7}$ is compared to $3.5 \times 10^{-4}$, we can divide the larger number by the smaller number:

$\text{Ratio} = \frac{3.5 \times 10^{-4}}{4 \times 10^{-7}}$

First, divide the coefficients:

$\frac{3.5}{4} = 0.875$

Next, divide the powers of 10:

$\frac{10^{-4}}{10^{-7}} = 10^{-4 - (-7)} = 10^{3}$

Now, multiply the results together:

$\text{Ratio} = 0.875 \times 10^{3} = 875$

Thus, $4 \times 10^{-7}$ is 875 times smaller than $3.5 \times 10^{-4}$.

Would you like more details or have any questions?

Here are 5 related questions:

1. What is the process for dividing numbers in scientific notation?
2. How do you multiply and divide powers of 10?
3. Can you explain how scientific notation works with very small or very large numbers?
4. What is the significance of the coefficient in scientific notation?
5. How can you compare two numbers with different exponents?

Tip: When dealing with scientific notation, always handle the coefficients and powers of 10 separately for clarity.