Standard and Expanded Form Worksheets - Free Printable

Problem Description:

The task involves converting numbers between standard form and expanded form. Here's a breakdown of the problem:

1. Expanded Form: Writing a number as the sum of the values of its digits based on their place values.
- Example: The number 345 in expanded form is \(300 + 40 + 5\).

2. Standard Form: Writing a number in its usual numeric form.
- Example: The expanded form \(300 + 40 + 5\) in standard form is 345.

The worksheet provides a list of numbers to convert to expanded form and some expressions to convert to standard form.

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Solution:

#### Part 1: Write in Expanded Form
We need to break down each number into its place values.

1. 657
- Hundreds place: \(6 \times 100 = 600\)
- Tens place: \(5 \times 10 = 50\)
- Ones place: \(7 \times 1 = 7\)
- Expanded form: \(600 + 50 + 7\)

2. 873
- Hundreds place: \(8 \times 100 = 800\)
- Tens place: \(7 \times 10 = 70\)
- Ones place: \(3 \times 1 = 3\)
- Expanded form: \(800 + 70 + 3\)

3. 64
- Tens place: \(6 \times 10 = 60\)
- Ones place: \(4 \times 1 = 4\)
- Expanded form: \(60 + 4\)

4. 326
- Hundreds place: \(3 \times 100 = 300\)
- Tens place: \(2 \times 10 = 20\)
- Ones place: \(6 \times 1 = 6\)
- Expanded form: \(300 + 20 + 6\)

5. 31
- Tens place: \(3 \times 10 = 30\)
- Ones place: \(1 \times 1 = 1\)
- Expanded form: \(30 + 1\)

6. 249
- Hundreds place: \(2 \times 100 = 200\)
- Tens place: \(4 \times 10 = 40\)
- Ones place: \(9 \times 1 = 9\)
- Expanded form: \(200 + 40 + 9\)

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#### Part 2: Write in Standard Form
We need to simplify the given expressions to find the standard form of the numbers.

1. \(500 + 80 + 4\)
- Combine the values: \(500 + 80 + 4 = 584\)
- Standard form: 584

2. \(900 + 50 + 6\)
- Combine the values: \(900 + 50 + 6 = 956\)
- Standard form: 956

3. \(400 + 20 \times 2\)
- Simplify the multiplication: \(20 \times 2 = 40\)
- Combine the values: \(400 + 40 = 440\)
- Standard form: 440

4. \(100 + 90 + 8\)
- Combine the values: \(100 + 90 + 8 = 198\)
- Standard form: 198

5. \(900 + 9\)
- Combine the values: \(900 + 9 = 909\)
- Standard form: 909

6. \(300 + 2\)
- Combine the values: \(300 + 2 = 302\)
- Standard form: 302

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Final Answers:

#### Expanded Form:
1. \(657 \rightarrow 600 + 50 + 7\)
2. \(873 \rightarrow 800 + 70 + 3\)
3. \(64 \rightarrow 60 + 4\)
4. \(326 \rightarrow 300 + 20 + 6\)
5. \(31 \rightarrow 30 + 1\)
6. \(249 \rightarrow 200 + 40 + 9\)

#### Standard Form:
1. \(500 + 80 + 4 \rightarrow 584\)
2. \(900 + 50 + 6 \rightarrow 956\)
3. \(400 + 20 \times 2 \rightarrow 440\)
4. \(100 + 90 + 8 \rightarrow 198\)
5. \(900 + 9 \rightarrow 909\)
6. \(300 + 2 \rightarrow 302\)

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Boxed Final Answer:

\[
\boxed{
\begin{array}{ll}
\text{Expanded Form:} & \\
1. & 600 + 50 + 7 \\
2. & 800 + 70 + 3 \\
3. & 60 + 4 \\
4. & 300 + 20 + 6 \\
5. & 30 + 1 \\
6. & 200 + 40 + 9 \\
\\
\text{Standard Form:} & \\
1. & 584 \\
2. & 956 \\
3. & 440 \\
4. & 198 \\
5. & 909 \\
6. & 302 \\
\end{array}
}
\]