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Let's go through the problems on the worksheet step by step. I'll start by evaluating the expressions and solving the problems provided.

### A. Divide the following decimals mentally:
1. \( 2.3 \div 0.1 \)
2. \( 75.653 \div 0.001 \)
3. \( 6.56 \div 0.01 \)
4. \( 95.87 \div 1.000 \)
5. \( 80.1 \div 10.000 \)

### Solutions:
1. **\( 2.3 \div 0.1 = 23 \)**
   - Dividing by 0.1 is the same as multiplying by 10.
2. **\( 75.653 \div 0.001 = 75653 \)**
   - Dividing by 0.001 is the same as multiplying by 1000.
3. **\( 6.56 \div 0.01 = 656 \)**
   - Dividing by 0.01 is the same as multiplying by 100.
4. **\( 95.87 \div 1.000 = 95.87 \)**
   - Dividing by 1 doesn't change the number.
5. **\( 80.1 \div 10.000 = 0.00801 \)**
   - Dividing by 10,000 moves the decimal point four places to the left.

### B. Find the quotient:
6. \( 9 \div 2.25 \)
7. \( 18.75 \div 2.50 \)
8. \( 29.21 \div 6.23 \)
9. \( 65.60 \div 4.56 \)
10. \( 133.75 \div 12.75 \)

### Solutions:
6. **\( 9 \div 2.25 = 4 \)**
   - 9 divided by 2.25 gives exactly 4.
7. **\( 18.75 \div 2.50 = 7.5 \)**
   - 18.75 divided by 2.50 results in 7.5.
8. **\( 29.21 \div 6.23 \approx 4.688 \)**
   - The division results in approximately 4.688.
9. **\( 65.60 \div 4.56 \approx 14.386 \)**
   - The quotient is approximately 14.386.
10. **\( 133.75 \div 12.75 \approx 10.49 \)**
    - The quotient is approximately 10.49.

Would you like more detailed explanations for any of these problems? If so, let me know!

### Follow-up Questions:
1. How do you adjust decimal places when dividing by 0.1 or 0.01?
2. What happens when dividing by a number slightly less than 1?
3. How does dividing a number by 1 affect its value?
4. How does dividing by a small decimal like 0.001 change the result?
5. What is the importance of precision when dealing with decimal division?

### Tip:
When dividing by decimals, converting the divisor into a whole number by multiplying both the numerator and the denominator by a power of 10 often simplifies the process.

Divide the following decimals mentally and find the quotient for the provided expressions.

Learn how to divide decimals and find quotients with a step-by-step guide. This worksheet covers key arithmetic concepts, including dividing by powers of ten and calculating exact quotients. Suitable for students in Grades 5-6.

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