This worksheet provides 12 vertical multiplication problems involving decimals for students to solve.

Problem: Solve the decimal multiplication problems and show your work.

#### Step-by-Step Solutions:

---

Problem 1: \( 164.00 \times 4.73 \)

1. Ignore the decimals and multiply as whole numbers:
\[
164 \times 473 = 77,592
\]

2. Count the total number of decimal places in the factors:
- \( 164.00 \) has 2 decimal places.
- \( 4.73 \) has 2 decimal places.
- Total: \( 2 + 2 = 4 \) decimal places.

3. Place the decimal point in the product:
\[
77,592 \rightarrow 775.92
\]

Answer:
\[
\boxed{775.92}
\]

---

Problem 2: \( 655.00 \times 1.53 \)

1. Ignore the decimals and multiply as whole numbers:
\[
655 \times 153 = 100,015
\]

2. Count the total number of decimal places in the factors:
- \( 655.00 \) has 2 decimal places.
- \( 1.53 \) has 2 decimal places.
- Total: \( 2 + 2 = 4 \) decimal places.

3. Place the decimal point in the product:
\[
100,015 \rightarrow 1000.15
\]

Answer:
\[
\boxed{1000.15}
\]

---

Problem 3: \( 360.00 \times 1.55 \)

1. Ignore the decimals and multiply as whole numbers:
\[
360 \times 155 = 55,800
\]

2. Count the total number of decimal places in the factors:
- \( 360.00 \) has 2 decimal places.
- \( 1.55 \) has 2 decimal places.
- Total: \( 2 + 2 = 4 \) decimal places.

3. Place the decimal point in the product:
\[
55,800 \rightarrow 558.00
\]

Answer:
\[
\boxed{558.00}
\]

---

Problem 4: \( 62.20 \times 55.10 \)

1. Ignore the decimals and multiply as whole numbers:
\[
622 \times 551 = 34,3322
\]

2. Count the total number of decimal places in the factors:
- \( 62.20 \) has 2 decimal places.
- \( 55.10 \) has 2 decimal places.
- Total: \( 2 + 2 = 4 \) decimal places.

3. Place the decimal point in the product:
\[
34,3322 \rightarrow 3433.22
\]

Answer:
\[
\boxed{3433.22}
\]

---

Problem 5: \( 9.37 \times 318.00 \)

1. Ignore the decimals and multiply as whole numbers:
\[
937 \times 318 = 297,666
\]

2. Count the total number of decimal places in the factors:
- \( 9.37 \) has 2 decimal places.
- \( 318.00 \) has 2 decimal places.
- Total: \( 2 + 2 = 4 \) decimal places.

3. Place the decimal point in the product:
\[
297,666 \rightarrow 2976.66
\]

Answer:
\[
\boxed{2976.66}
\]

---

Problem 6: \( 239.00 \times 9.91 \)

1. Ignore the decimals and multiply as whole numbers:
\[
239 \times 991 = 236,849
\]

2. Count the total number of decimal places in the factors:
- \( 239.00 \) has 2 decimal places.
- \( 9.91 \) has 2 decimal places.
- Total: \( 2 + 2 = 4 \) decimal places.

3. Place the decimal point in the product:
\[
236,849 \rightarrow 2368.49
\]

Answer:
\[
\boxed{2368.49}
\]

---

Problem 7: \( 7.28 \times 157.00 \)

1. Ignore the decimals and multiply as whole numbers:
\[
728 \times 157 = 114,376
\]

2. Count the total number of decimal places in the factors:
- \( 7.28 \) has 2 decimal places.
- \( 157.00 \) has 2 decimal places.
- Total: \( 2 + 2 = 4 \) decimal places.

3. Place the decimal point in the product:
\[
114,376 \rightarrow 1143.76
\]

Answer:
\[
\boxed{1143.76}
\]

---

Problem 8: \( 73.40 \times 80.80 \)

1. Ignore the decimals and multiply as whole numbers:
\[
734 \times 808 = 593,272
\]

2. Count the total number of decimal places in the factors:
- \( 73.40 \) has 2 decimal places.
- \( 80.80 \) has 2 decimal places.
- Total: \( 2 + 2 = 4 \) decimal places.

3. Place the decimal point in the product:
\[
593,272 \rightarrow 5932.72
\]

Answer:
\[
\boxed{5932.72}
\]

---

Problem 9: \( 173.00 \times 6.45 \)

1. Ignore the decimals and multiply as whole numbers:
\[
173 \times 645 = 112,035
\]

2. Count the total number of decimal places in the factors:
- \( 173.00 \) has 2 decimal places.
- \( 6.45 \) has 2 decimal places.
- Total: \( 2 + 2 = 4 \) decimal places.

3. Place the decimal point in the product:
\[
112,035 \rightarrow 1120.35
\]

Answer:
\[
\boxed{1120.35}
\]

---

Problem 10: \( 138.00 \times 8.13 \)

1. Ignore the decimals and multiply as whole numbers:
\[
138 \times 813 = 112,254
\]

2. Count the total number of decimal places in the factors:
- \( 138.00 \) has 2 decimal places.
- \( 8.13 \) has 2 decimal places.
- Total: \( 2 + 2 = 4 \) decimal places.

3. Place the decimal point in the product:
\[
112,254 \rightarrow 1122.54
\]

Answer:
\[
\boxed{1122.54}
\]

---

Problem 11: \( 410.00 \times 4.16 \)

1. Ignore the decimals and multiply as whole numbers:
\[
410 \times 416 = 170,560
\]

2. Count the total number of decimal places in the factors:
- \( 410.00 \) has 2 decimal places.
- \( 4.16 \) has 2 decimal places.
- Total: \( 2 + 2 = 4 \) decimal places.

3. Place the decimal point in the product:
\[
170,560 \rightarrow 1705.60
\]

Answer:
\[
\boxed{1705.60}
\]

---

Problem 12: \( 78.40 \times 53.30 \)

1. Ignore the decimals and multiply as whole numbers:
\[
784 \times 533 = 41,8072
\]

2. Count the total number of decimal places in the factors:
- \( 78.40 \) has 2 decimal places.
- \( 53.30 \) has 2 decimal places.
- Total: \( 2 + 2 = 4 \) decimal places.

3. Place the decimal point in the product:
\[
41,8072 \rightarrow 4180.72
\]

Answer:
\[
\boxed{4180.72}
\]

---

Final Answers:

\[
\boxed{
\begin{aligned}
1. & \ 775.92 \\
2. & \ 1000.15 \\
3. & \ 558.00 \\
4. & \ 3433.22 \\
5. & \ 2976.66 \\
6. & \ 2368.49 \\
7. & \ 1143.76 \\
8. & \ 5932.72 \\
9. & \ 1120.35 \\
10. & \ 1122.54 \\
11. & \ 1705.60 \\
12. & \ 4180.72 \\
\end{aligned}
}
\]