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To complete the place-value table showing the powers of 10, let's fill in the blanks by following the instructions to divide by 10 as indicated.

Starting from the leftmost side:

1. The number to the left of 100 is \(1000\) because \(1000 \div 10 = 100\).
2. The number to the right of \(\frac{1}{10000}\) is \(\frac{1}{100000}\) because \(\frac{1}{10000} \div 10 = \frac{1}{100000}\).

Now let's confirm and fill in each column:
- The first column will have \(1000\) at the top and \(10^3\) at the bottom.
- The last column will have \(\frac{1}{100000}\) at the top and \(10^{-5}\) at the bottom.

Here's the completed table:

\[
\begin{array}{|c|c|c|c|c|c|c|c|c|c|}
\hline
1000 & 100 & 10 & 1 & \frac{1}{10} & \frac{1}{100} & \frac{1}{1000} & \frac{1}{10000} & \frac{1}{100000} \\ \hline
10^3 & 10^2 & 10^1 & 10^0 & 10^{-1} & 10^{-2} & 10^{-3} & 10^{-4} & 10^{-5} \\ \hline
\end{array}
\]

Would you like further details or explanations on this topic?

Here are five relative questions to consider:
1. What happens when you multiply instead of divide each step by 10?
2. How would the table change if we used a different base, like 2, instead of 10?
3. Can you explain the significance of \(10^0\) being equal to 1?
4. How does this table relate to scientific notation?
5. What are the real-world applications of understanding powers of 10?

**Tip:** Understanding powers of 10 is fundamental in scientific notation, which simplifies working with very large or very small numbers.

Complete the place-value table showing the powers of 10.

Learn how to complete the place-value table with powers of 10. This problem covers the concept of powers of 10 and how dividing by 10 affects the value. Suitable for students in Grades 4-6.

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