Grade 6 Decimals Worksheet: Multiplying decimals in columns.

Problem: Multiplying Decimals in Columns

The task involves solving the multiplication problems for decimals, as shown in the worksheet. Below is a step-by-step explanation of how to solve each problem.

---

#### 1. \( 8.1 \times 0.900 \)

- Step 1: Ignore the decimal points and multiply the numbers as whole numbers:
\[
81 \times 900 = 72900
\]

- Step 2: Count the total number of decimal places in both numbers:
- \( 8.1 \) has 1 decimal place.
- \( 0.900 \) has 3 decimal places.
- Total decimal places = \( 1 + 3 = 4 \).

- Step 3: Place the decimal point in the product so that there are 4 decimal places:
\[
72900 \rightarrow 7.2900
\]

- Final Answer:
\[
8.1 \times 0.900 = 7.2900
\]

---

#### 2. \( 0.0661 \times 0.200 \)

- Step 1: Ignore the decimal points and multiply the numbers as whole numbers:
\[
661 \times 200 = 132200
\]

- Step 2: Count the total number of decimal places in both numbers:
- \( 0.0661 \) has 4 decimal places.
- \( 0.200 \) has 3 decimal places.
- Total decimal places = \( 4 + 3 = 7 \).

- Step 3: Place the decimal point in the product so that there are 7 decimal places:
\[
132200 \rightarrow 0.0132200
\]

- Final Answer:
\[
0.0661 \times 0.200 = 0.0132200
\]

---

#### 3. \( 5 \times 2.2 \)

- Step 1: Ignore the decimal points and multiply the numbers as whole numbers:
\[
5 \times 22 = 110
\]

- Step 2: Count the total number of decimal places in both numbers:
- \( 5 \) has 0 decimal places.
- \( 2.2 \) has 1 decimal place.
- Total decimal places = \( 0 + 1 = 1 \).

- Step 3: Place the decimal point in the product so that there is 1 decimal place:
\[
110 \rightarrow 11.0
\]

- Final Answer:
\[
5 \times 2.2 = 11.0
\]

---

#### 4. \( 0.83 \times 0.0100 \)

- Step 1: Ignore the decimal points and multiply the numbers as whole numbers:
\[
83 \times 100 = 8300
\]

- Step 2: Count the total number of decimal places in both numbers:
- \( 0.83 \) has 2 decimal places.
- \( 0.0100 \) has 4 decimal places.
- Total decimal places = \( 2 + 4 = 6 \).

- Step 3: Place the decimal point in the product so that there are 6 decimal places:
\[
8300 \rightarrow 0.083000
\]

- Final Answer:
\[
0.83 \times 0.0100 = 0.008300
\]

---

#### 5. \( 0.0080 \times 0.700 \)

- Step 1: Ignore the decimal points and multiply the numbers as whole numbers:
\[
80 \times 700 = 56000
\]

- Step 2: Count the total number of decimal places in both numbers:
- \( 0.0080 \) has 4 decimal places.
- \( 0.700 \) has 3 decimal places.
- Total decimal places = \( 4 + 3 = 7 \).

- Step 3: Place the decimal point in the product so that there are 7 decimal places:
\[
56000 \rightarrow 0.0056000
\]

- Final Answer:
\[
0.0080 \times 0.700 = 0.0056000
\]

---

#### 6. \( 0.0079 \times 50.0 \)

- Step 1: Ignore the decimal points and multiply the numbers as whole numbers:
\[
79 \times 500 = 39500
\]

- Step 2: Count the total number of decimal places in both numbers:
- \( 0.0079 \) has 4 decimal places.
- \( 50.0 \) has 1 decimal place.
- Total decimal places = \( 4 + 1 = 5 \).

- Step 3: Place the decimal point in the product so that there are 5 decimal places:
\[
39500 \rightarrow 0.39500
\]

- Final Answer:
\[
0.0079 \times 50.0 = 0.39500
\]

---

#### 7. \( 0.0082 \times 40.0 \)

- Step 1: Ignore the decimal points and multiply the numbers as whole numbers:
\[
82 \times 400 = 32800
\]

- Step 2: Count the total number of decimal places in both numbers:
- \( 0.0082 \) has 4 decimal places.
- \( 40.0 \) has 1 decimal place.
- Total decimal places = \( 4 + 1 = 5 \).

- Step 3: Place the decimal point in the product so that there are 5 decimal places:
\[
32800 \rightarrow 0.32800
\]

- Final Answer:
\[
0.0082 \times 40.0 = 0.32800
\]

---

#### 8. \( 0.033 \times 0.0500 \)

- Step 1: Ignore the decimal points and multiply the numbers as whole numbers:
\[
33 \times 500 = 16500
\]

- Step 2: Count the total number of decimal places in both numbers:
- \( 0.033 \) has 3 decimal places.
- \( 0.0500 \) has 4 decimal places.
- Total decimal places = \( 3 + 4 = 7 \).

- Step 3: Place the decimal point in the product so that there are 7 decimal places:
\[
16500 \rightarrow 0.0016500
\]

- Final Answer:
\[
0.033 \times 0.0500 = 0.0016500
\]

---

#### 9. \( 0.0063 \times 0.0600 \)

- Step 1: Ignore the decimal points and multiply the numbers as whole numbers:
\[
63 \times 600 = 37800
\]

- Step 2: Count the total number of decimal places in both numbers:
- \( 0.0063 \) has 4 decimal places.
- \( 0.0600 \) has 4 decimal places.
- Total decimal places = \( 4 + 4 = 8 \).

- Step 3: Place the decimal point in the product so that there are 8 decimal places:
\[
37800 \rightarrow 0.00037800
\]

- Final Answer:
\[
0.0063 \times 0.0600 = 0.00037800
\]

---

Final Answers:

\[
\boxed{
\begin{array}{ll}
1. & 7.2900 \\
2. & 0.0132200 \\
3. & 11.0 \\
4. & 0.008300 \\
5. & 0.0056000 \\
6. & 0.39500 \\
7. & 0.32800 \\
8. & 0.0016500 \\
9. & 0.00037800 \\
\end{array}
}
\]