To determine how many times smaller [tex]\(4 \times 10^{-7}\)[/tex] is than [tex]\(3.5 \times 10^{-4}\)[/tex], we can divide the larger number by the smaller number. Here's a step-by-step explanation:
1. Identify the numbers:
- The smaller number: [tex]\(4 \times 10^{-7}\)[/tex]
- The larger number: [tex]\(3.5 \times 10^{-4}\)[/tex]
2. Set up the division:
We want to find how many times smaller [tex]\(4 \times 10^{-7}\)[/tex] is than [tex]\(3.5 \times 10^{-4}\)[/tex], which can be expressed as:
[tex]\[
\text{Result} = \frac{3.5 \times 10^{-4}}{4 \times 10^{-7}}
\][/tex]
3. Simplify the division:
- Divide the coefficients (numerical parts) first:
[tex]\[
\frac{3.5}{4} = 0.875
\][/tex]
- Next, divide the powers of ten. Recall that when you divide exponents with the same base, you subtract the exponents:
[tex]\[
10^{-4} \div 10^{-7} = 10^{-4 - (-7)} = 10^{-4 + 7} = 10^3
\][/tex]
Combining these results, we get:
[tex]\[
0.875 \times 10^3
\][/tex]
4. Express the final result:
[tex]\[
0.875 \times 10^3 = 875
\][/tex]
Therefore, [tex]\(4 \times 10^{-7}\)[/tex] is 875 times smaller than [tex]\(3.5 \times 10^{-4}\)[/tex].
So, the correct answer is:
[tex]\[ \boxed{875} \][/tex]
