Place Value Worksheets -Worksheets Library - Free Printable

Decimal Place Value Worksheet Solution

#### 1) Write each number in expanded form.

To write a number in expanded form, we break it down into the value of each digit based on its place value.

a) 673.12
- The digit 6 is in the hundreds place: \(6 \times 100\)
- The digit 7 is in the tens place: \(7 \times 10\)
- The digit 3 is in the ones place: \(3 \times 1\)
- The digit 1 is in the tenths place: \(1 \times 0.1\)
- The digit 2 is in the hundredths place: \(2 \times 0.01\)

So, the expanded form is:
\[
673.12 = (6 \times 100) + (7 \times 10) + (3 \times 1) + (1 \times 0.1) + (2 \times 0.01)
\]

b) 866.81
- The digit 8 is in the hundreds place: \(8 \times 100\)
- The digit 6 is in the tens place: \(6 \times 10\)
- The digit 6 is in the ones place: \(6 \times 1\)
- The digit 8 is in the tenths place: \(8 \times 0.1\)
- The digit 1 is in the hundredths place: \(1 \times 0.01\)

So, the expanded form is:
\[
866.81 = (8 \times 100) + (6 \times 10) + (6 \times 1) + (8 \times 0.1) + (1 \times 0.01)
\]

c) 244.37
- The digit 2 is in the hundreds place: \(2 \times 100\)
- The digit 4 is in the tens place: \(4 \times 10\)
- The digit 4 is in the ones place: \(4 \times 1\)
- The digit 3 is in the tenths place: \(3 \times 0.1\)
- The digit 7 is in the hundredths place: \(7 \times 0.01\)

So, the expanded form is:
\[
244.37 = (2 \times 100) + (4 \times 10) + (4 \times 1) + (3 \times 0.1) + (7 \times 0.01)
\]

d) 130.78
- The digit 1 is in the hundreds place: \(1 \times 100\)
- The digit 3 is in the tens place: \(3 \times 10\)
- The digit 0 is in the ones place: \(0 \times 1\)
- The digit 7 is in the tenths place: \(7 \times 0.1\)
- The digit 8 is in the hundredths place: \(8 \times 0.01\)

So, the expanded form is:
\[
130.78 = (1 \times 100) + (3 \times 10) + (0 \times 1) + (7 \times 0.1) + (8 \times 0.01)
\]

e) 145.69
- The digit 1 is in the hundreds place: \(1 \times 100\)
- The digit 4 is in the tens place: \(4 \times 10\)
- The digit 5 is in the ones place: \(5 \times 1\)
- The digit 6 is in the tenths place: \(6 \times 0.1\)
- The digit 9 is in the hundredths place: \(9 \times 0.01\)

So, the expanded form is:
\[
145.69 = (1 \times 100) + (4 \times 10) + (5 \times 1) + (6 \times 0.1) + (9 \times 0.01)
\]

f) 429.67
- The digit 4 is in the hundreds place: \(4 \times 100\)
- The digit 2 is in the tens place: \(2 \times 10\)
- The digit 9 is in the ones place: \(9 \times 1\)
- The digit 6 is in the tenths place: \(6 \times 0.1\)
- The digit 7 is in the hundredths place: \(7 \times 0.01\)

So, the expanded form is:
\[
429.67 = (4 \times 100) + (2 \times 10) + (9 \times 1) + (6 \times 0.1) + (7 \times 0.01)
\]

---

#### 2) Write each number in standard form.

To write a number in standard form, we combine all the parts given in the expanded form.

a) \((7 \times 100) + (2 \times 10) + (5 \times 1) + (3 \times 0.1) + (9 \times 0.01) + (7 \times 0.001)\)
- \(7 \times 100 = 700\)
- \(2 \times 10 = 20\)
- \(5 \times 1 = 5\)
- \(3 \times 0.1 = 0.3\)
- \(9 \times 0.01 = 0.09\)
- \(7 \times 0.001 = 0.007\)

Adding these together:
\[
700 + 20 + 5 + 0.3 + 0.09 + 0.007 = 725.397
\]

So, the standard form is:
\[
725.397
\]

b) \((4 \times 1000) + (0 \times 100) + (0 \times 10) + (1 \times 1) + (3 \times 0.1) + (9 \times 0.01)\)
- \(4 \times 1000 = 4000\)
- \(0 \times 100 = 0\)
- \(0 \times 10 = 0\)
- \(1 \times 1 = 1\)
- \(3 \times 0.1 = 0.3\)
- \(9 \times 0.01 = 0.09\)

Adding these together:
\[
4000 + 0 + 0 + 1 + 0.3 + 0.09 = 4001.39
\]

So, the standard form is:
\[
4001.39
\]

c) \((5 \times 100) + (1 \times 10) + (3 \times 1) + (2 \times 0.1) + (0 \times 0.01) + (1 \times 0.001)\)
- \(5 \times 100 = 500\)
- \(1 \times 10 = 10\)
- \(3 \times 1 = 3\)
- \(2 \times 0.1 = 0.2\)
- \(0 \times 0.01 = 0\)
- \(1 \times 0.001 = 0.001\)

Adding these together:
\[
500 + 10 + 3 + 0.2 + 0 + 0.001 = 513.201
\]

So, the standard form is:
\[
513.201
\]

d) \((3 \times 1000) + (9 \times 100) + (7 \times 10) + (8 \times 1) + (7 \times 0.1) + (7 \times 0.01)\)
- \(3 \times 1000 = 3000\)
- \(9 \times 100 = 900\)
- \(7 \times 10 = 70\)
- \(8 \times 1 = 8\)
- \(7 \times 0.1 = 0.7\)
- \(7 \times 0.01 = 0.07\)

Adding these together:
\[
3000 + 900 + 70 + 8 + 0.7 + 0.07 = 3978.77
\]

So, the standard form is:
\[
3978.77
\]

---

#### 3) Find the missing numbers.

a) \(0.3 + 0.008 = \_\_\_\_\_\_\_\_\_\)
- Adding \(0.3\) and \(0.008\):
\[
0.3 + 0.008 = 0.308
\]

So, the answer is:
\[
0.308
\]

b) \(4 + 0.067 + \_\_\_\_\_\_\_\_\_\_ = 4.167\)
- Let the missing number be \(x\). We have:
\[
4 + 0.067 + x = 4.167
\]
- Subtract \(4 + 0.067\) from both sides:
\[
x = 4.167 - 4.067 = 0.1
\]

So, the answer is:
\[
0.1
\]

c) \(\_\_\_\_\_\_\_\_\_\_ + 8 + 0.8 = 8.87\)
- Let the missing number be \(x\). We have:
\[
x + 8 + 0.8 = 8.87
\]
- Combine \(8\) and \(0.8\):
\[
x + 8.8 = 8.87
\]
- Subtract \(8.8\) from both sides:
\[
x = 8.87 - 8.8 = 0.07
\]

So, the answer is:
\[
0.07
\]

d) \(\_\_\_\_\_\_\_\_\_\_ = 5 + 0.007\)
- Simplify the right-hand side:
\[
5 + 0.007 = 5.007
\]

So, the answer is:
\[
5.007
\]

e) \(9.327 = \_\_\_\_\_\_\_\_\_\_ + 9 + 0.007\)
- Let the missing number be \(x\). We have:
\[
x + 9 + 0.007 = 9.327
\]
- Combine \(9\) and \(0.007\):
\[
x + 9.007 = 9.327
\]
- Subtract \(9.007\) from both sides:
\[
x = 9.327 - 9.007 = 0.32
\]

So, the answer is:
\[
0.32
\]

f) \(8.392 = 8.002 + \_\_\_\_\_\_\_\_\_\_\)
- Let the missing number be \(x\). We have:
\[
8.002 + x = 8.392
\]
- Subtract \(8.002\) from both sides:
\[
x = 8.392 - 8.002 = 0.39
\]

So, the answer is:
\[
0.39
\]

---

Final Answers:

1. Expanded forms:
- a) \(673.12 = (6 \times 100) + (7 \times 10) + (3 \times 1) + (1 \times 0.1) + (2 \times 0.01)\)
- b) \(866.81 = (8 \times 100) + (6 \times 10) + (6 \times 1) + (8 \times 0.1) + (1 \times 0.01)\)
- c) \(244.37 = (2 \times 100) + (4 \times 10) + (4 \times 1) + (3 \times 0.1) + (7 \times 0.01)\)
- d) \(130.78 = (1 \times 100) + (3 \times 10) + (0 \times 1) + (7 \times 0.1) + (8 \times 0.01)\)
- e) \(145.69 = (1 \times 100) + (4 \times 10) + (5 \times 1) + (6 \times 0.1) + (9 \times 0.01)\)
- f) \(429.67 = (4 \times 100) + (2 \times 10) + (9 \times 1) + (6 \times 0.1) + (7 \times 0.01)\)

2. Standard forms:
- a) \(725.397\)
- b) \(4001.39\)
- c) \(513.201\)
- d) \(3978.77\)

3. Missing numbers:
- a) \(0.308\)
- b) \(0.1\)
- c) \(0.07\)
- d) \(5.007\)
- e) \(0.32\)
- f) \(0.39\)

\boxed{
\begin{array}{l}
\text{1. Expanded forms:} \\
\text{a) } (6 \times 100) + (7 \times 10) + (3 \times 1) + (1 \times 0.1) + (2 \times 0.01) \\
\text{b) } (8 \times 100) + (6 \times 10) + (6 \times 1) + (8 \times 0.1) + (1 \times 0.01) \\
\text{c) } (2 \times 100) + (4 \times 10) + (4 \times 1) + (3 \times 0.1) + (7 \times 0.01) \\
\text{d) } (1 \times 100) + (3 \times 10) + (0 \times 1) + (7 \times 0.1) + (8 \times 0.01) \\
\text{e) } (1 \times 100) + (4 \times 10) + (5 \times 1) + (6 \times 0.1) + (9 \times 0.01) \\
\text{f) } (4 \times 100) + (2 \times 10) + (9 \times 1) + (6 \times 0.1) + (7 \times 0.01) \\
\\
\text{2. Standard forms:} \\
\text{a) } 725.397 \\
\text{b) } 4001.39 \\
\text{c) } 513.201 \\
\text{d) } 3978.77 \\
\\
\text{3. Missing numbers:} \\
\text{a) } 0.308 \\
\text{b) } 0.1 \\
\text{c) } 0.07 \\
\text{d) } 5.007 \\
\text{e) } 0.32 \\
\text{f) } 0.39 \\
\end{array}
}