Decimals in Standard and Expanded Form Worksheets - Free Printable

Problem Overview:

The task involves two main parts:
1. Writing numbers in expanded form.
2. Writing expressions in standard form.

Let's solve each part step by step.

---

Part 1: Writing Numbers in Expanded Form

#### Expanded Form:
In expanded form, a number is written as the sum of the values of its digits based on their place values.

#### Solutions:

1. 689.435:
- Break down the number into its place values:
- 600 (hundreds)
- 80 (tens)
- 9 (ones)
- 0.4 (tenths)
- 0.03 (hundredths)
- 0.005 (thousandths)
- Expanded form:
$$
600 + 80 + 9 + 0.4 + 0.03 + 0.005
$$

2. 24.17:
- Break down the number into its place values:
- 20 (tens)
- 4 (ones)
- 0.1 (tenths)
- 0.07 (hundredths)
- Expanded form:
$$
20 + 4 + 0.1 + 0.07
$$

3. 36.9:
- Break down the number into its place values:
- 30 (tens)
- 6 (ones)
- 0.9 (tenths)
- Expanded form:
$$
30 + 6 + 0.9
$$

4. 1.824:
- Break down the number into its place values:
- 1 (ones)
- 0.8 (tenths)
- 0.02 (hundredths)
- 0.004 (thousandths)
- Expanded form:
$$
1 + 0.8 + 0.02 + 0.004
$$

5. 709.63:
- Break down the number into its place values:
- 700 (hundreds)
- 0 (tens)
- 9 (ones)
- 0.6 (tenths)
- 0.03 (hundredths)
- Expanded form:
$$
700 + 0 + 9 + 0.6 + 0.03
$$

6. 8.6:
- Break down the number into its place values:
- 8 (ones)
- 0.6 (tenths)
- Expanded form:
$$
8 + 0.6
$$

---

Part 2: Writing Expressions in Standard Form

#### Standard Form:
In standard form, an expression is simplified to a single numerical value.

#### Solutions:

1. 200 + 10 + 6 + 0.3:
- Add all the terms together:
$$
200 + 10 + 6 + 0.3 = 216.3
$$
- Standard form:
$$
216.3
$$

2. 4 + 0.9 + 0.008:
- Add all the terms together:
$$
4 + 0.9 + 0.008 = 4.908
$$
- Standard form:
$$
4.908
$$

3. 50 + 2 + 0.6:
- Add all the terms together:
$$
50 + 2 + 0.6 = 52.6
$$
- Standard form:
$$
52.6
$$

4. 900 + 30 + 7 + 0.2 + 0.01:
- Add all the terms together:
$$
900 + 30 + 7 + 0.2 + 0.01 = 937.21
$$
- Standard form:
$$
937.21
$$

5. 80 + 8 + 0.1 + 0.05:
- Add all the terms together:
$$
80 + 8 + 0.1 + 0.05 = 88.15
$$
- Standard form:
$$
88.15
$$

6. 300 + 70 + 1 + 0.08 + 0.009:
- Add all the terms together:
$$
300 + 70 + 1 + 0.08 + 0.009 = 371.089
$$
- Standard form:
$$
371.089
$$

---

Final Answers:

#### Part 1: Expanded Form
1. $ 600 + 80 + 9 + 0.4 + 0.03 + 0.005 $
2. $ 20 + 4 + 0.1 + 0.07 $
3. $ 30 + 6 + 0.9 $
4. $ 1 + 0.8 + 0.02 + 0.004 $
5. $ 700 + 0 + 9 + 0.6 + 0.03 $
6. $ 8 + 0.6 $

#### Part 2: Standard Form
1. $ 216.3 $
2. $ 4.908 $
3. $ 52.6 $
4. $ 937.21 $
5. $ 88.15 $
6. $ 371.089 $

---

Boxed Final Answer:

$$
\boxed{
\begin{array}{ll}
\text{Part 1:} & \text{1. } 600 + 80 + 9 + 0.4 + 0.03 + 0.005 \\
& \text{2. } 20 + 4 + 0.1 + 0.07 \\
& \text{3. } 30 + 6 + 0.9 \\
& \text{4. } 1 + 0.8 + 0.02 + 0.004 \\
& \text{5. } 700 + 0 + 9 + 0.6 + 0.03 \\
& \text{6. } 8 + 0.6 \\
\text{Part 2:} & \text{1. } 216.3 \\
& \text{2. } 4.908 \\
& \text{3. } 52.6 \\
& \text{4. } 937.21 \\
& \text{5. } 88.15 \\
& \text{6. } 371.089 \\
\end{array}
}
$$