Math Problem Statement

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

Solution

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 10001000 because 1000÷10=1001000 \div 10 = 100.
  2. The number to the right of 110000\frac{1}{10000} is 1100000\frac{1}{100000} because 110000÷10=1100000\frac{1}{10000} \div 10 = \frac{1}{100000}.

Now let's confirm and fill in each column:

  • The first column will have 10001000 at the top and 10310^3 at the bottom.
  • The last column will have 1100000\frac{1}{100000} at the top and 10510^{-5} at the bottom.

Here's the completed table:

\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.

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Math Problem Analysis

Mathematical Concepts

Place value system
Powers of 10
Division and multiplication by powers of 10

Formulas

10^n where n is the power
Dividing by 10 decreases the power by 1
Multiplying by 10 increases the power by 1

Theorems

Basic exponent rules

Suitable Grade Level

Grades 4-6