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Complete the pattern: \( 0.9017 \div 10=\square \) \( 90.17 \div 1,000=\square \) \( 901.7 \div 10,000=\square \) \( 9,017 \div 100,000=\square \)

Ask by Santiago Hampton. in the United States
Jan 23,2025

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Answer

All divisions result in \( 0.09017 \).

Solution

Let's analyze and complete the given pattern by performing each division: 1. **\( 0.9017 \div 10 \)** - Dividing by 10 shifts the decimal point one place to the left. - \( 0.9017 \div 10 = 0.09017 \) 2. **\( 90.17 \div 1,000 \)** - Dividing by 1,000 shifts the decimal point three places to the left. - \( 90.17 \div 1,000 = 0.09017 \) 3. **\( 901.7 \div 10,000 \)** - Dividing by 10,000 shifts the decimal point four places to the left. - \( 901.7 \div 10,000 = 0.09017 \) 4. **\( 9,017 \div 100,000 \)** - Dividing by 100,000 shifts the decimal point five places to the left. - \( 9,017 \div 100,000 = 0.09017 \) **Completed Pattern:** \[ \begin{align*} 0.9017 \div 10 &= 0.09017 \\ 90.17 \div 1,000 &= 0.09017 \\ 901.7 \div 10,000 &= 0.09017 \\ 9,017 \div 100,000 &= 0.09017 \\ \end{align*} \] All divisions result in the same value, \( 0.09017 \), demonstrating the consistency of the pattern.

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The pattern in the division shows a sequence where the numbers are either multiplied or divided by a factor of 10, leading the decimal point to shift left with each subsequent division. To complete the pattern: - \( 0.9017 \div 10 = 0.09017 \) - \( 90.17 \div 1,000 = 0.09017 \) - \( 901.7 \div 10,000 = 0.09017 \) - \( 9,017 \div 100,000 = 0.09017 \) Each division results in the same answer: \( 0.09017 \).

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