Question
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Complete the pattern: \[ \begin{array}{r}\square \div 10=4.751 \\ \square \div 10=47.51 \\ \square \div 10=475.1 \\ \div 10=4,751\end{array} \]

Ask by Harper Lynch. in the United States
Jan 23,2025

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Tutor-Verified Answer

Answer

The squares are filled with the numbers 47.51, 475.1, 4751, and 47510 respectively.

Solution

Let's analyze the given pattern step by step: \[ \begin{array}{r} \square \div 10 = 4.751 \\ \square \div 10 = 47.51 \\ \square \div 10 = 475.1 \\ \div 10 = 4,751 \end{array} \] ### Step 1: - **Equation:** \(\square \div 10 = 4.751\) - **Solution:** To find the value of the square, multiply both sides by 10. \[ \square = 4.751 \times 10 = 47.51 \] ### Step 2: - **Equation:** \(\square \div 10 = 47.51\) - **Solution:** Multiply both sides by 10. \[ \square = 47.51 \times 10 = 475.1 \] ### Step 3: - **Equation:** \(\square \div 10 = 475.1\) - **Solution:** Multiply both sides by 10. \[ \square = 475.1 \times 10 = 4751 \] ### Step 4: - **Equation:** \(\div 10 = 4,751\) - **Interpretation:** This implies that before dividing by 10, the number was 47,510. \[ \square = 4,751 \times 10 = 47,510 \] ### Completed Pattern: \[ \begin{array}{r} 47.51 \div 10 = 4.751 \\ 475.1 \div 10 = 47.51 \\ 4751 \div 10 = 475.1 \\ 47510 \div 10 = 4751 \end{array} \] ### Summary: Each step involves multiplying the previous number by 10 to get the next number in the pattern. Therefore, the sequence of numbers filling the squares is as follows: 1. **First Square:** 47.51 2. **Second Square:** 475.1 3. **Third Square:** 4751 4. **Fourth Square:** 47510

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Bonus Knowledge

The pattern in the equations shows that each time you divide by 10, the number moves the decimal point to the left. To solve for the missing values, you need to simply multiply 10 back into each value on the right side of the equations. Starting with the first equation: 1. \( \square \div 10 = 4.751 \) → \( \square = 4.751 \times 10 = 47.51 \) 2. \( \square \div 10 = 47.51 \) → \( \square = 47.51 \times 10 = 475.1 \) 3. \( \square \div 10 = 475.1 \) → \( \square = 475.1 \times 10 = 4751 \) Therefore, the complete pattern is: \[ \begin{array}{r}\text{47.51} \\ \text{475.1} \\ \text{4751} \end{array} \]

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