Multiplying 2-Digit by 2-Digit Numbers with Various Decimal Places (A) - Free Printable

The task involves multiplying 2-digit numbers with various decimal places. Below, I will solve each multiplication problem step by step and explain the process.

General Steps for Multiplying Decimals:

1. Ignore the decimals: Multiply the numbers as if they were whole numbers.
2. Count the total number of decimal places: Add up the number of decimal places in both numbers being multiplied.
3. Place the decimal point: Place the decimal point in the product so that the total number of decimal places matches the sum from step 2.

---

Problem 1: \( 2.3 \times 4.6 \)

- Step 1: Ignore the decimals and multiply \( 23 \times 46 \):
\[
23 \times 46 = 1058
\]
- Step 2: Count the decimal places. \( 2.3 \) has 1 decimal place, and \( 4.6 \) has 1 decimal place. Total: \( 1 + 1 = 2 \).
- Step 3: Place the decimal point in the product:
\[
1058 \rightarrow 10.58
\]
- Answer: \( 10.58 \)

---

Problem 2: \( 0.67 \times 0.50 \)

- Step 1: Ignore the decimals and multiply \( 67 \times 50 \):
\[
67 \times 50 = 3350
\]
- Step 2: Count the decimal places. \( 0.67 \) has 2 decimal places, and \( 0.50 \) has 2 decimal places. Total: \( 2 + 2 = 4 \).
- Step 3: Place the decimal point in the product:
\[
3350 \rightarrow 0.3350 \text{ (or simply } 0.335\text{)}
\]
- Answer: \( 0.335 \)

---

Problem 3: \( 0.27 \times 73 \)

- Step 1: Ignore the decimals and multiply \( 27 \times 73 \):
\[
27 \times 73 = 1971
\]
- Step 2: Count the decimal places. \( 0.27 \) has 2 decimal places, and \( 73 \) has 0 decimal places. Total: \( 2 + 0 = 2 \).
- Step 3: Place the decimal point in the product:
\[
1971 \rightarrow 19.71
\]
- Answer: \( 19.71 \)

---

Problem 4: \( 2.8 \times 32 \)

- Step 1: Ignore the decimals and multiply \( 28 \times 32 \):
\[
28 \times 32 = 896
\]
- Step 2: Count the decimal places. \( 2.8 \) has 1 decimal place, and \( 32 \) has 0 decimal places. Total: \( 1 + 0 = 1 \).
- Step 3: Place the decimal point in the product:
\[
896 \rightarrow 89.6
\]
- Answer: \( 89.6 \)

---

Problem 5: \( 3.1 \times 94 \)

- Step 1: Ignore the decimals and multiply \( 31 \times 94 \):
\[
31 \times 94 = 2914
\]
- Step 2: Count the decimal places. \( 3.1 \) has 1 decimal place, and \( 94 \) has 0 decimal places. Total: \( 1 + 0 = 1 \).
- Step 3: Place the decimal point in the product:
\[
2914 \rightarrow 291.4
\]
- Answer: \( 291.4 \)

---

Problem 6: \( 6.5 \times 6.6 \)

- Step 1: Ignore the decimals and multiply \( 65 \times 66 \):
\[
65 \times 66 = 4290
\]
- Step 2: Count the decimal places. \( 6.5 \) has 1 decimal place, and \( 6.6 \) has 1 decimal place. Total: \( 1 + 1 = 2 \).
- Step 3: Place the decimal point in the product:
\[
4290 \rightarrow 42.90 \text{ (or simply } 42.9\text{)}
\]
- Answer: \( 42.9 \)

---

Problem 7: \( 3.3 \times 0.89 \)

- Step 1: Ignore the decimals and multiply \( 33 \times 89 \):
\[
33 \times 89 = 2937
\]
- Step 2: Count the decimal places. \( 3.3 \) has 1 decimal place, and \( 0.89 \) has 2 decimal places. Total: \( 1 + 2 = 3 \).
- Step 3: Place the decimal point in the product:
\[
2937 \rightarrow 2.937
\]
- Answer: \( 2.937 \)

---

Problem 8: \( 48 \times 48 \)

- Step 1: Multiply \( 48 \times 48 \):
\[
48 \times 48 = 2304
\]
- Step 2: Count the decimal places. Both numbers have 0 decimal places. Total: \( 0 + 0 = 0 \).
- Step 3: No decimal point needed:
\[
2304
\]
- Answer: \( 2304 \)

---

Problem 9: \( 5.4 \times 0.19 \)

- Step 1: Ignore the decimals and multiply \( 54 \times 19 \):
\[
54 \times 19 = 1026
\]
- Step 2: Count the decimal places. \( 5.4 \) has 1 decimal place, and \( 0.19 \) has 2 decimal places. Total: \( 1 + 2 = 3 \).
- Step 3: Place the decimal point in the product:
\[
1026 \rightarrow 1.026
\]
- Answer: \( 1.026 \)

---

Problem 10: \( 47 \times 14 \)

- Step 1: Multiply \( 47 \times 14 \):
\[
47 \times 14 = 658
\]
- Step 2: Count the decimal places. Both numbers have 0 decimal places. Total: \( 0 + 0 = 0 \).
- Step 3: No decimal point needed:
\[
658
\]
- Answer: \( 658 \)

---

Problem 11: \( 5.8 \times 4.3 \)

- Step 1: Ignore the decimals and multiply \( 58 \times 43 \):
\[
58 \times 43 = 2494
\]
- Step 2: Count the decimal places. \( 5.8 \) has 1 decimal place, and \( 4.3 \) has 1 decimal place. Total: \( 1 + 1 = 2 \).
- Step 3: Place the decimal point in the product:
\[
2494 \rightarrow 24.94
\]
- Answer: \( 24.94 \)

---

Problem 12: \( 0.46 \times 0.50 \)

- Step 1: Ignore the decimals and multiply \( 46 \times 50 \):
\[
46 \times 50 = 2300
\]
- Step 2: Count the decimal places. \( 0.46 \) has 2 decimal places, and \( 0.50 \) has 2 decimal places. Total: \( 2 + 2 = 4 \).
- Step 3: Place the decimal point in the product:
\[
2300 \rightarrow 0.2300 \text{ (or simply } 0.23\text{)}
\]
- Answer: \( 0.23 \)

---

Problem 13: \( 53 \times 7.8 \)

- Step 1: Ignore the decimals and multiply \( 53 \times 78 \):
\[
53 \times 78 = 4134
\]
- Step 2: Count the decimal places. \( 53 \) has 0 decimal places, and \( 7.8 \) has 1 decimal place. Total: \( 0 + 1 = 1 \).
- Step 3: Place the decimal point in the product:
\[
4134 \rightarrow 413.4
\]
- Answer: \( 413.4 \)

---

Problem 14: \( 3.0 \times 0.49 \)

- Step 1: Ignore the decimals and multiply \( 30 \times 49 \):
\[
30 \times 49 = 1470
\]
- Step 2: Count the decimal places. \( 3.0 \) has 1 decimal place, and \( 0.49 \) has 2 decimal places. Total: \( 1 + 2 = 3 \).
- Step 3: Place the decimal point in the product:
\[
1470 \rightarrow 1.470 \text{ (or simply } 1.47\text{)}
\]
- Answer: \( 1.47 \)

---

Problem 15: \( 87 \times 0.21 \)

- Step 1: Ignore the decimals and multiply \( 87 \times 21 \):
\[
87 \times 21 = 1827
\]
- Step 2: Count the decimal places. \( 87 \) has 0 decimal places, and \( 0.21 \) has 2 decimal places. Total: \( 0 + 2 = 2 \).
- Step 3: Place the decimal point in the product:
\[
1827 \rightarrow 18.27
\]
- Answer: \( 18.27 \)

---

Problem 16: \( 47 \times 0.12 \)

- Step 1: Ignore the decimals and multiply \( 47 \times 12 \):
\[
47 \times 12 = 564
\]
- Step 2: Count the decimal places. \( 47 \) has 0 decimal places, and \( 0.12 \) has 2 decimal places. Total: \( 0 + 2 = 2 \).
- Step 3: Place the decimal point in the product:
\[
564 \rightarrow 5.64
\]
- Answer: \( 5.64 \)

---

Problem 17: \( 84 \times 18 \)

- Step 1: Multiply \( 84 \times 18 \):
\[
84 \times 18 = 1512
\]
- Step 2: Count the decimal places. Both numbers have 0 decimal places. Total: \( 0 + 0 = 0 \).
- Step 3: No decimal point needed:
\[
1512
\]
- Answer: \( 1512 \)

---

Problem 18: \( 6.7 \times 0.95 \)

- Step 1: Ignore the decimals and multiply \( 67 \times 95 \):
\[
67 \times 95 = 6365
\]
- Step 2: Count the decimal places. \( 6.7 \) has 1 decimal place, and \( 0.95 \) has 2 decimal places. Total: \( 1 + 2 = 3 \).
- Step 3: Place the decimal point in the product:
\[
6365 \rightarrow 6.365
\]
- Answer: \( 6.365 \)

---

Problem 19: \( 0.83 \times 8.9 \)

- Step 1: Ignore the decimals and multiply \( 83 \times 89 \):
\[
83 \times 89 = 7387
\]
- Step 2: Count the decimal places. \( 0.83 \) has 2 decimal places, and \( 8.9 \) has 1 decimal place. Total: \( 2 + 1 = 3 \).
- Step 3: Place the decimal point in the product:
\[
7387 \rightarrow 7.387
\]
- Answer: \( 7.387 \)

---

Problem 20: \( 1.2 \times 0.54 \)

- Step 1: Ignore the decimals and multiply \( 12 \times 54 \):
\[
12 \times 54 = 648
\]
- Step 2: Count the decimal places. \( 1.2 \) has 1 decimal place, and \( 0.54 \) has 2 decimal places. Total: \( 1 + 2 = 3 \).
- Step 3: Place the decimal point in the product:
\[
648 \rightarrow 0.648
\]
- Answer: \( 0.648 \)

---

Problem 21: \( 0.13 \times 4.3 \)

- Step 1: Ignore the decimals and multiply \( 13 \times 43 \):
\[
13 \times 43 = 559
\]
- Step 2: Count the decimal places. \( 0.13 \) has 2 decimal places, and \( 4.3 \) has 1 decimal place. Total: \( 2 + 1 = 3 \).
- Step 3: Place the decimal point in the product:
\[
559 \rightarrow 0.559
\]
- Answer: \( 0.559 \)

---

Problem 22: \( 0.89 \times 0.34 \)

- Step 1: Ignore the decimals and multiply \( 89 \times 34 \):
\[
89 \times 34 = 3026
\]
- Step 2: Count the decimal places. \( 0.89 \) has 2 decimal places, and \( 0.34 \) has 2 decimal places. Total: \( 2 + 2 = 4 \).
- Step 3: Place the decimal point in the product:
\[
3026 \rightarrow 0.3026
\]
- Answer: \( 0.3026 \)

---

Problem 23: \( 0.31 \times 0.93 \)

- Step 1: Ignore the decimals and multiply \( 31 \times 93 \):
\[
31 \times 93 = 2883
\]
- Step 2: Count the decimal places. \( 0.31 \) has 2 decimal places, and \( 0.93 \) has 2 decimal places. Total: \( 2 + 2 = 4 \).
- Step 3: Place the decimal point in the product:
\[
2883 \rightarrow 0.2883
\]
- Answer: \( 0.2883 \)

---

Problem 24: \( 8.1 \times 16 \)

- Step 1: Ignore the decimals and multiply \( 81 \times 16 \):
\[
81 \times 16 = 1296
\]
- Step 2: Count the decimal places. \( 8.1 \) has 1 decimal place, and \( 16 \) has 0 decimal places. Total: \( 1 + 0 = 1 \).
- Step 3: Place the decimal point in the product:
\[
1296 \rightarrow 129.6
\]
- Answer: \( 129.6 \)

---

Problem 25: \( 13 \times 0.76 \)

- Step 1: Ignore the decimals and multiply \( 13 \times 76 \):
\[
13 \times 76 = 988
\]
- Step 2: Count the decimal places. \( 13 \) has 0 decimal places, and \( 0.76 \) has 2 decimal places. Total: \( 0 + 2 = 2 \).
- Step 3: Place the decimal point in the product:
\[
988 \rightarrow 9.88
\]
- Answer: \( 9.88 \)

---

Final Answers:

\[
\boxed{
\begin{array}{ll}
10.58 & 0.335 \\
19.71 & 89.6 \\
291.4 & 42.9 \\
2.937 & 2304 \\
1.026 & 658 \\
24.94 & 0.23 \\
413.4 & 1.47 \\
18.27 & 5.64 \\
1512 & 6.365 \\
7.387 & 0.648 \\
0.559 & 0.3026 \\
0.2883 & 129.6 \\
9.88 &
\end{array}
}
\]