Expanded Notation Using Decimals worksheet with 20 problems for converting between standard and expanded forms.

Problem Overview:

The task involves two parts:
1. Writing numbers in expanded notation using decimals.
2. Writing each number in standard form from its expanded notation.

Let's solve each part step by step.

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Part 1: Writing Numbers in Expanded Notation Using Decimals

#### Expanded Notation Explanation:
In expanded notation, a number is broken down into the sum of its place values. For example:
- The number 566.63 can be written as:
$$
5 \times 100 + 6 \times 10 + 6 \times 1 + 6 \times 0.1 + 3 \times 0.01
$$

#### Solutions:

1. 566.63
$$
5 \times 100 + 6 \times 10 + 6 \times 1 + 6 \times 0.1 + 3 \times 0.01
$$

2. 851.18
$$
8 \times 100 + 5 \times 10 + 1 \times 1 + 1 \times 0.1 + 8 \times 0.01
$$

3. 783.62
$$
7 \times 100 + 8 \times 10 + 3 \times 1 + 6 \times 0.1 + 2 \times 0.01
$$

4. 416.82
$$
4 \times 100 + 1 \times 10 + 6 \times 1 + 8 \times 0.1 + 2 \times 0.01
$$

5. 842.74
$$
8 \times 100 + 4 \times 10 + 2 \times 1 + 7 \times 0.1 + 4 \times 0.01
$$

6. 244.60
$$
2 \times 100 + 4 \times 10 + 4 \times 1 + 6 \times 0.1 + 0 \times 0.01
$$

7. 120.77
$$
1 \times 100 + 2 \times 10 + 0 \times 1 + 7 \times 0.1 + 7 \times 0.01
$$

8. 866.57
$$
8 \times 100 + 6 \times 10 + 6 \times 1 + 5 \times 0.1 + 7 \times 0.01
$$

9. 145.36
$$
1 \times 100 + 4 \times 10 + 5 \times 1 + 3 \times 0.1 + 6 \times 0.01
$$

10. 426.57
$$
4 \times 100 + 2 \times 10 + 6 \times 1 + 5 \times 0.1 + 7 \times 0.01
$$

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Part 2: Writing Each Number in Standard Form

#### Standard Form Explanation:
In standard form, we combine the expanded notation back into a single decimal number. For example:
- The expanded notation (9 × 100) + (7 × 10) + (6 × 1) + (9 × 0.1) + (7 × 0.01) becomes:
$$
900 + 70 + 6 + 0.9 + 0.07 = 976.97
$$

#### Solutions:

11. (9 × 100) + (7 × 10) + (6 × 1) + (9 × 0.1) + (7 × 0.01)
$$
900 + 70 + 6 + 0.9 + 0.07 = 976.97
$$

12. (5 × 100) + (5 × 10) + (5 × 1) + (5 × 0.1) + (1 × 0.01)
$$
500 + 50 + 5 + 0.5 + 0.01 = 555.51
$$

13. (5 × 100) + (4 × 10) + (4 × 1) + (3 × 0.1) + (0 × 0.01)
$$
500 + 40 + 4 + 0.3 + 0 = 544.3
$$

14. (1 × 100) + (1 × 10) + (4 × 1) + (7 × 0.1) + (9 × 0.01)
$$
100 + 10 + 4 + 0.7 + 0.09 = 114.79
$$

15. (2 × 100) + (2 × 10) + (0 × 1) + (4 × 0.1) + (9 × 0.01)
$$
200 + 20 + 0 + 0.4 + 0.09 = 220.49
$$

16. (4 × 100) + (4 × 10) + (0 × 1) + (7 × 0.1) + (7 × 0.01)
$$
400 + 40 + 0 + 0.7 + 0.07 = 440.77
$$

17. (4 × 100) + (6 × 10) + (3 × 1) + (4 × 0.1) + (8 × 0.01)
$$
400 + 60 + 3 + 0.4 + 0.08 = 463.48
$$

18. (9 × 100) + (7 × 10) + (8 × 1) + (7 × 0.1) + (7 × 0.01)
$$
900 + 70 + 8 + 0.7 + 0.07 = 978.77
$$

19. (1 × 100) + (1 × 10) + (8 × 1) + (2 × 0.1) + (7 × 0.01)
$$
100 + 10 + 8 + 0.2 + 0.07 = 118.27
$$

20. (9 × 100) + (5 × 10) + (8 × 1) + (5 × 0.1) + (2 × 0.01)
$$
900 + 50 + 8 + 0.5 + 0.02 = 958.52
$$

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Final Answers:

#### Part 1: Expanded Notation
1. $ 5 \times 100 + 6 \times 10 + 6 \times 1 + 6 \times 0.1 + 3 \times 0.01 $
2. $ 8 \times 100 + 5 \times 10 + 1 \times 1 + 1 \times 0.1 + 8 \times 0.01 $
3. $ 7 \times 100 + 8 \times 10 + 3 \times 1 + 6 \times 0.1 + 2 \times 0.01 $
4. $ 4 \times 100 + 1 \times 10 + 6 \times 1 + 8 \times 0.1 + 2 \times 0.01 $
5. $ 8 \times 100 + 4 \times 10 + 2 \times 1 + 7 \times 0.1 + 4 \times 0.01 $
6. $ 2 \times 100 + 4 \times 10 + 4 \times 1 + 6 \times 0.1 + 0 \times 0.01 $
7. $ 1 \times 100 + 2 \times 10 + 0 \times 1 + 7 \times 0.1 + 7 \times 0.01 $
8. $ 8 \times 100 + 6 \times 10 + 6 \times 1 + 5 \times 0.1 + 7 \times 0.01 $
9. $ 1 \times 100 + 4 \times 10 + 5 \times 1 + 3 \times 0.1 + 6 \times 0.01 $
10. $ 4 \times 100 + 2 \times 10 + 6 \times 1 + 5 \times 0.1 + 7 \times 0.01 $

#### Part 2: Standard Form
11. $ 976.97 $
12. $ 555.51 $
13. $ 544.3 $
14. $ 114.79 $
15. $ 220.49 $
16. $ 440.77 $
17. $ 463.48 $
18. $ 978.77 $
19. $ 118.27 $
20. $ 958.52 $

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Boxed Final Answers:

$$
\boxed{
\begin{array}{ll}
\text{Part 1:} & \text{See detailed expanded notations above.} \\
\text{Part 2:} & 976.97, 555.51, 544.3, 114.79, 220.49, 440.77, 463.48, 978.77, 118.27, 958.52 \\
\end{array}
}
$$