Question
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
Real Tutor Solution
Tutor-Verified Answer
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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Extra Insights
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: \( 0.09017 \).