Decimal Place Value Worksheets - Math Monks - Free Printable

Problem Analysis:

The worksheet involves two main tasks:
1. Writing numbers in expanded form: Breaking down a given decimal number into its component parts based on place value.
2. Writing expressions in standard form: Converting an expanded form expression back into a single decimal number.

Let's solve each part step by step.

---

Part 1: Write in Expanded Form

#### a) 63.87
- Step 1: Identify the place value of each digit.
- 6 is in the tens place: \(6 \times 10\)
- 3 is in the ones place: \(3 \times 1\)
- 8 is in the tenths place: \(8 \times \frac{1}{10}\)
- 7 is in the hundredths place: \(7 \times \frac{1}{100}\)
- Expanded Form:
\[
63.87 = (6 \times 10) + (3 \times 1) + (8 \times \frac{1}{10}) + (7 \times \frac{1}{100})
\]

#### b) 3.04
- Step 1: Identify the place value of each digit.
- 3 is in the ones place: \(3 \times 1\)
- 0 is in the tenths place: \(0 \times \frac{1}{10}\)
- 4 is in the hundredths place: \(4 \times \frac{1}{100}\)
- Expanded Form:
\[
3.04 = (3 \times 1) + (0 \times \frac{1}{10}) + (4 \times \frac{1}{100})
\]

#### c) 8.7
- Step 1: Identify the place value of each digit.
- 8 is in the ones place: \(8 \times 1\)
- 7 is in the tenths place: \(7 \times \frac{1}{10}\)
- Expanded Form:
\[
8.7 = (8 \times 1) + (7 \times \frac{1}{10})
\]

#### d) 0.87
- Step 1: Identify the place value of each digit.
- 8 is in the tenths place: \(8 \times \frac{1}{10}\)
- 7 is in the hundredths place: \(7 \times \frac{1}{100}\)
- Expanded Form:
\[
0.87 = (8 \times \frac{1}{10}) + (7 \times \frac{1}{100})
\]

#### e) 380.17
- Step 1: Identify the place value of each digit.
- 3 is in the hundreds place: \(3 \times 100\)
- 8 is in the tens place: \(8 \times 10\)
- 0 is in the ones place: \(0 \times 1\)
- 1 is in the tenths place: \(1 \times \frac{1}{10}\)
- 7 is in the hundredths place: \(7 \times \frac{1}{100}\)
- Expanded Form:
\[
380.17 = (3 \times 100) + (8 \times 10) + (0 \times 1) + (1 \times \frac{1}{10}) + (7 \times \frac{1}{100})
\]

---

Part 2: Write in Standard Form

#### a) \((2 \times 100) + (9 \times 10) + (3 \times 1)\)
- Step 1: Calculate each term.
- \(2 \times 100 = 200\)
- \(9 \times 10 = 90\)
- \(3 \times 1 = 3\)
- Step 2: Add the results.
\[
200 + 90 + 3 = 293
\]
- Standard Form:
\[
293
\]

#### b) \((8 \times 1000) + (4 \times 10) + (3 \times 1) + \left(2 \times \frac{1}{100}\right)\)
- Step 1: Calculate each term.
- \(8 \times 1000 = 8000\)
- \(4 \times 10 = 40\)
- \(3 \times 1 = 3\)
- \(2 \times \frac{1}{100} = 0.02\)
- Step 2: Add the results.
\[
8000 + 40 + 3 + 0.02 = 8043.02
\]
- Standard Form:
\[
8043.02
\]

#### c) \((6 \times 100) + (7 \times 10) + (4 \times 1) + \left(6 \times \frac{1}{1000}\right)\)
- Step 1: Calculate each term.
- \(6 \times 100 = 600\)
- \(7 \times 10 = 70\)
- \(4 \times 1 = 4\)
- \(6 \times \frac{1}{1000} = 0.006\)
- Step 2: Add the results.
\[
600 + 70 + 4 + 0.006 = 674.006
\]
- Standard Form:
\[
674.006
\]

#### d) \((6 \times 1000) + \left(3 \times \frac{1}{10}\right)\)
- Step 1: Calculate each term.
- \(6 \times 1000 = 6000\)
- \(3 \times \frac{1}{10} = 0.3\)
- Step 2: Add the results.
\[
6000 + 0.3 = 6000.3
\]
- Standard Form:
\[
6000.3
\]

#### e) \((5 \times 1000) + (9 \times 100) + (3 \times 1) + \left(3 \times \frac{1}{10}\right)\)
- Step 1: Calculate each term.
- \(5 \times 1000 = 5000\)
- \(9 \times 100 = 900\)
- \(3 \times 1 = 3\)
- \(3 \times \frac{1}{10} = 0.3\)
- Step 2: Add the results.
\[
5000 + 900 + 3 + 0.3 = 5903.3
\]
- Standard Form:
\[
5903.3
\]

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Final Answers:

#### Part 1: Expanded Form
1. \(63.87 = (6 \times 10) + (3 \times 1) + (8 \times \frac{1}{10}) + (7 \times \frac{1}{100})\)
2. \(3.04 = (3 \times 1) + (0 \times \frac{1}{10}) + (4 \times \frac{1}{100})\)
3. \(8.7 = (8 \times 1) + (7 \times \frac{1}{10})\)
4. \(0.87 = (8 \times \frac{1}{10}) + (7 \times \frac{1}{100})\)
5. \(380.17 = (3 \times 100) + (8 \times 10) + (0 \times 1) + (1 \times \frac{1}{10}) + (7 \times \frac{1}{100})\)

#### Part 2: Standard Form
1. \((2 \times 100) + (9 \times 10) + (3 \times 1) = 293\)
2. \((8 \times 1000) + (4 \times 10) + (3 \times 1) + \left(2 \times \frac{1}{100}\right) = 8043.02\)
3. \((6 \times 100) + (7 \times 10) + (4 \times 1) + \left(6 \times \frac{1}{1000}\right) = 674.006\)
4. \((6 \times 1000) + \left(3 \times \frac{1}{10}\right) = 6000.3\)
5. \((5 \times 1000) + (9 \times 100) + (3 \times 1) + \left(3 \times \frac{1}{10}\right) = 5903.3\)

---

Boxed Final Answers:

\[
\boxed{
\begin{array}{ll}
\text{Part 1:} & \text{a) } (6 \times 10) + (3 \times 1) + (8 \times \frac{1}{10}) + (7 \times \frac{1}{100}) \\
& \text{b) } (3 \times 1) + (0 \times \frac{1}{10}) + (4 \times \frac{1}{100}) \\
& \text{c) } (8 \times 1) + (7 \times \frac{1}{10}) \\
& \text{d) } (8 \times \frac{1}{10}) + (7 \times \frac{1}{100}) \\
& \text{e) } (3 \times 100) + (8 \times 10) + (0 \times 1) + (1 \times \frac{1}{10}) + (7 \times \frac{1}{100}) \\
\text{Part 2:} & \text{a) } 293 \\
& \text{b) } 8043.02 \\
& \text{c) } 674.006 \\
& \text{d) } 6000.3 \\
& \text{e) } 5903.3 \\
\end{array}
}
\]