To determine which power of 10 would have a value of [tex]\(\frac{1}{1,000,000}\)[/tex], we can examine the pattern in the table:
[tex]\[
\begin{array}{|c|c|}
\hline
\text{Power of 10} & \text{Value} \\
\hline
10^1 & 10 \\
\hline
10^0 & 1 \\
\hline
10^{-1} & \frac{1}{10} \\
\hline
10^{-2} & \frac{1}{100} \\
\hline
10^{-3} & \frac{1}{1,000} \\
\hline
10^{-4} & \frac{1}{10,000} \\
\hline
\end{array}
\][/tex]
We can observe that each negative power of 10 corresponds to the reciprocal of a positive power of 10:
- [tex]\(10^{-1} = \frac{1}{10}\)[/tex]
- [tex]\(10^{-2} = \frac{1}{100}\)[/tex]
- [tex]\(10^{-3} = \frac{1}{1,000}\)[/tex]
- [tex]\(10^{-4} = \frac{1}{10,000}\)[/tex]
From this pattern, we can see that as the negative exponent increases by 1, the value becomes the reciprocal of an additional factor of 10.
To find the power of 10 corresponding to [tex]\(\frac{1}{1,000,000}\)[/tex]:
[tex]\[
1,000,000 = 10^6
\][/tex]
So the reciprocal of [tex]\(10^6\)[/tex] would be:
[tex]\[
\frac{1}{10^6} = 10^{-6}
\][/tex]
Therefore, the power of 10 that corresponds to the value of [tex]\(\frac{1}{1,000,000}\)[/tex] is [tex]\(\boxed{10^{-6}}\)[/tex].
Thus, [tex]\(\frac{1}{1,000,000}\)[/tex] corresponds to [tex]\(10^{-6}\)[/tex], and the value of [tex]\(\frac{1}{1,000,000}\)[/tex] is [tex]\(1 \times 10^{-6}\)[/tex] or [tex]\(1e-06\)[/tex].
