Math worksheet for practicing place value up to three decimal places with visual aids and calculations.

Problem Overview:

The worksheet focuses on understanding place value and converting numbers represented in expanded form into decimal notation. The tasks involve interpreting the place values (tens, ones, tenths, hundredths, thousandths) and performing calculations based on these values.

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Solution to Each Part:

#### Part 1: Place Value Conversion
We need to convert the given place value representations into decimal numbers.

##### Question 1:
- Given:
- Tens: 0
- Ones: 5
- Tenths: 7
- Hundredths: 3
- Thousandths: 2
- Calculation:
\( 5 + 0.7 + 0.03 + 0.002 = 5.732 \)
- Answer:
\( 5.732 \)

##### Question 2:
- Given:
- Thousands: 0
- Hundreds: 0
- Tens: 0
- Ones: 2
- Tenths: 0
- Hundredths: 4
- Thousandths: 3
- Calculation:
\( 2 + 0.04 + 0.003 = 2.043 \)
- Answer:
\( 2.043 \)

##### Question 3:
- Given:
- Tens: 0
- Ones: 6
- Tenths: 0
- Hundredths: 8
- Thousandths: 0
- Calculation:
\( 6 + 0.08 = 6.08 \)
- Answer:
\( 6.08 \)

##### Question 4:
- Given:
- Tens: 0
- Ones: 1
- Tenths: 6
- Hundredths: 0
- Thousandths: 3
- Calculation:
\( 1 + 0.6 + 0.003 = 1.603 \)
- Answer:
\( 1.603 \)

##### Question 5:
- Given:
- Tens: 0
- Ones: 4
- Tenths: 0
- Hundredths: 7
- Thousandths: 0
- Calculation:
\( 4 + 0.07 = 4.07 \)
- Answer:
\( 4.07 \)

##### Question 6:
- Given:
- Tens: 0
- Ones: 0
- Tenths: 0
- Hundredths: 9
- Thousandths: 5
- Calculation:
\( 0 + 0.09 + 0.005 = 0.095 \)
- Answer:
\( 0.095 \)

##### Question 7:
- Given:
- Tens: 0
- Ones: 7
- Tenths: 8
- Hundredths: 4
- Thousandths: 0
- Calculation:
\( 7 + 0.8 + 0.04 = 7.84 \)
- Answer:
\( 7.84 \)

##### Question 8:
- Given:
- Tens: 0
- Ones: 0
- Tenths: 9
- Hundredths: 0
- Thousandths: 3
- Calculation:
\( 0 + 0.9 + 0.003 = 0.903 \)
- Answer:
\( 0.903 \)

##### Question 9:
- Given:
- Tens: 0
- Ones: 0
- Tenths: 5
- Hundredths: 6
- Thousandths: 0
- Calculation:
\( 0 + 0.5 + 0.06 = 0.56 \)
- Answer:
\( 0.56 \)

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#### Part 2: Calculations
We need to perform the given calculations and express the answers as decimals.

##### Question 11:
- Given:
\( 9 \times 1 + 8 \times \frac{1}{10} + 2 \times \frac{1}{100} + 1 \times \frac{1}{1000} \)
- Calculation:
\( 9 + 0.8 + 0.02 + 0.001 = 9.821 \)
- Answer:
\( 9.821 \)

##### Question 12:
- Given:
\( 5 \times 1 + 4 \times \frac{1}{10} + 3 \times \frac{1}{100} + 2 \times \frac{1}{1000} \)
- Calculation:
\( 5 + 0.4 + 0.03 + 0.002 = 5.432 \)
- Answer:
\( 5.432 \)

##### Question 13:
- Given:
\( 7 \times 1 + 1 \times \frac{1}{100} \)
- Calculation:
\( 7 + 0.01 = 7.01 \)
- Answer:
\( 7.01 \)

##### Question 14:
- Given:
\( 5 \times \frac{1}{10} + 3 \times \frac{1}{100} + 2 \times \frac{1}{1000} \)
- Calculation:
\( 0.5 + 0.03 + 0.002 = 0.532 \)
- Answer:
\( 0.532 \)

##### Question 15:
- Given:
\( 3 \times \frac{1}{10} + 2 \times \frac{1}{100} + 9 \times \frac{1}{1000} \)
- Calculation:
\( 0.3 + 0.02 + 0.009 = 0.329 \)
- Answer:
\( 0.329 \)

##### Question 16:
- Given:
\( 2 \times 1 + 5 \times \frac{1}{10} + 8 \times \frac{1}{100} + 3 \times \frac{1}{1000} \)
- Calculation:
\( 2 + 0.5 + 0.08 + 0.003 = 2.583 \)
- Answer:
\( 2.583 \)

##### Question 17:
- Given:
\( 3 \times 1 + 2 \times \frac{1}{10} + 8 \times \frac{1}{1000} \)
- Calculation:
\( 3 + 0.2 + 0.008 = 3.208 \)
- Answer:
\( 3.208 \)

##### Question 18:
- Given:
\( 4 \times 10 + 2 \times 1 + 3 \times \frac{1}{100} + 7 \times \frac{1}{1000} \)
- Calculation:
\( 40 + 2 + 0.03 + 0.007 = 42.037 \)
- Answer:
\( 42.037 \)

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Final Answers:

1. \( 5.732 \)
2. \( 2.043 \)
3. \( 6.08 \)
4. \( 1.603 \)
5. \( 4.07 \)
6. \( 0.095 \)
7. \( 7.84 \)
8. \( 0.903 \)
9. \( 0.56 \)
11. \( 9.821 \)
12. \( 5.432 \)
13. \( 7.01 \)
14. \( 0.532 \)
15. \( 0.329 \)
16. \( 2.583 \)
17. \( 3.208 \)
18. \( 42.037 \)

\boxed{5.732, 2.043, 6.08, 1.603, 4.07, 0.095, 7.84, 0.903, 0.56, 9.821, 5.432, 7.01, 0.532, 0.329, 2.583, 3.208, 42.037}