Question
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Complete the pattern: \( \begin{array}{l}960.4 \div \square=96.04 \\ 9,604 \div \square=96.04 \\ 96,040 \div \square=96.04 \\ 9,604,000 \div \square=96.04\end{array} \)

Ask by Ramirez Peters. in the United States
Jan 23,2025

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Tutor-Verified Answer

Answer

The denominators are 10, 100, 1,000, and 100,000 respectively.

Solution

To complete the pattern, we need to determine the denominators (\(\square\)) that satisfy each equation so that the result is \(96.04\). Let's analyze each equation: 1. **First Equation:** \[ 960.4 \div \square = 96.04 \] To find \(\square\): \[ \square = \frac{960.4}{96.04} = 10 \] 2. **Second Equation:** \[ 9,604 \div \square = 96.04 \] To find \(\square\): \[ \square = \frac{9,604}{96.04} = 100 \] 3. **Third Equation:** \[ 96,040 \div \square = 96.04 \] To find \(\square\): \[ \square = \frac{96,040}{96.04} = 1,000 \] 4. **Fourth Equation:** \[ 9,604,000 \div \square = 96.04 \] To find \(\square\): \[ \square = \frac{9,604,000}{96.04} = 100,000 \] **Pattern Observation:** - The denominators are increasing by factors of 10 each time: - \(10\), \(100\), \(1,000\), \(100,000\) **Completed Pattern:** \[ \begin{array}{l} 960.4 \div 10 = 96.04 \\ 9,604 \div 100 = 96.04 \\ 96,040 \div 1,000 = 96.04 \\ 9,604,000 \div 100,000 = 96.04 \end{array} \]

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Bonus Knowledge

To find the missing value in each equation, we need to identify the relationship that ties all the numbers to the constant result of 96.04. 1. For the first equation, \( 960.4 \div \square = 96.04 \). We can solve for the missing value: \[ \square = \frac{960.4}{96.04} = 10. \] 2. In the second equation, \( 9,604 \div \square = 96.04 \): \[ \square = \frac{9,604}{96.04} = 100. \] 3. For the third equation, \( 96,040 \div \square = 96.04 \): \[ \square = \frac{96,040}{96.04} = 1,000. \] 4. Lastly, in the equation \( 9,604,000 \div \square = 96.04 \): \[ \square = \frac{9,604,000}{96.04} = 10,000. \] Thus, the pattern for the values in the square is: 10, 100, 1000, and 10,000 respectively. The complete pattern can be represented as: \( \begin{array}{l}960.4 \div 10=96.04 \\ 9,604 \div 100=96.04 \\ 96,040 \div 1,000=96.04 \\ 9,604,000 \div 10,000=96.04\end{array} \)

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