Grade 6 Math Worksheets: Multiplying decimals with missing factors ... - Free Printable

To solve the problems involving multiplying decimals, we follow these steps:

1. Ignore the decimal points and multiply the numbers as if they were whole numbers.
2. Count the total number of decimal places in the factors being multiplied.
3. Place the decimal point in the product so that the total number of decimal places in the product equals the sum of the decimal places in the factors.

Let's solve each problem step by step:

---

Problem 1: \( 12.56 \times 3.4 \)

1. Ignore the decimal points: \( 1256 \times 34 \).
\[
1256 \times 34 = 42704
\]
2. Count the decimal places:
- \( 12.56 \) has 2 decimal places.
- \( 3.4 \) has 1 decimal place.
- Total: \( 2 + 1 = 3 \) decimal places.
3. Place the decimal point:
\[
42704 \rightarrow 42.704
\]

Answer: \( 42.704 \)

---

Problem 2: \( 15.38 \times 5.32 \)

1. Ignore the decimal points: \( 1538 \times 532 \).
\[
1538 \times 532 = 819056
\]
2. Count the decimal places:
- \( 15.38 \) has 2 decimal places.
- \( 5.32 \) has 2 decimal places.
- Total: \( 2 + 2 = 4 \) decimal places.
3. Place the decimal point:
\[
819056 \rightarrow 81.9056
\]

Answer: \( 81.9056 \)

---

Problem 3: \( 7.5 \times 2.8 \)

1. Ignore the decimal points: \( 75 \times 28 \).
\[
75 \times 28 = 2100
\]
2. Count the decimal places:
- \( 7.5 \) has 1 decimal place.
- \( 2.8 \) has 1 decimal place.
- Total: \( 1 + 1 = 2 \) decimal places.
3. Place the decimal point:
\[
2100 \rightarrow 21.00
\]

Answer: \( 21.00 \)

---

Problem 4: \( 3.282 \times 19.4 \)

1. Ignore the decimal points: \( 3282 \times 194 \).
\[
3282 \times 194 = 636668
\]
2. Count the decimal places:
- \( 3.282 \) has 3 decimal places.
- \( 19.4 \) has 1 decimal place.
- Total: \( 3 + 1 = 4 \) decimal places.
3. Place the decimal point:
\[
636668 \rightarrow 63.6668
\]

Answer: \( 63.6668 \)

---

Problem 5: \( 7.948 \times 2.8 \)

1. Ignore the decimal points: \( 7948 \times 28 \).
\[
7948 \times 28 = 222544
\]
2. Count the decimal places:
- \( 7.948 \) has 3 decimal places.
- \( 2.8 \) has 1 decimal place.
- Total: \( 3 + 1 = 4 \) decimal places.
3. Place the decimal point:
\[
222544 \rightarrow 22.2544
\]

Answer: \( 22.2544 \)

---

Problem 6: \( 24.38 \times 100 \)

1. Ignore the decimal points: \( 2438 \times 100 \).
\[
2438 \times 100 = 243800
\]
2. Count the decimal places:
- \( 24.38 \) has 2 decimal places.
- \( 100 \) has 0 decimal places.
- Total: \( 2 + 0 = 2 \) decimal places.
3. Place the decimal point:
\[
243800 \rightarrow 2438.00
\]

Answer: \( 2438.00 \)

---

Problem 7: \( 0.082 \times 0.621 \)

1. Ignore the decimal points: \( 82 \times 621 \).
\[
82 \times 621 = 51042
\]
2. Count the decimal places:
- \( 0.082 \) has 3 decimal places.
- \( 0.621 \) has 3 decimal places.
- Total: \( 3 + 3 = 6 \) decimal places.
3. Place the decimal point:
\[
51042 \rightarrow 0.051042
\]

Answer: \( 0.051042 \)

---

Problem 8: \( 3.7 \times 97.8 \)

1. Ignore the decimal points: \( 37 \times 978 \).
\[
37 \times 978 = 36186
\]
2. Count the decimal places:
- \( 3.7 \) has 1 decimal place.
- \( 97.8 \) has 1 decimal place.
- Total: \( 1 + 1 = 2 \) decimal places.
3. Place the decimal point:
\[
36186 \rightarrow 361.86
\]

Answer: \( 361.86 \)

---

Problem 9: \( 0.052 \times 4.18 \)

1. Ignore the decimal points: \( 52 \times 418 \).
\[
52 \times 418 = 21736
\]
2. Count the decimal places:
- \( 0.052 \) has 3 decimal places.
- \( 4.18 \) has 2 decimal places.
- Total: \( 3 + 2 = 5 \) decimal places.
3. Place the decimal point:
\[
21736 \rightarrow 0.21736
\]

Answer: \( 0.21736 \)

---

Final Answers:

\[
\boxed{
\begin{array}{ll}
1) & 42.704 \\
2) & 81.9056 \\
3) & 21.00 \\
4) & 63.6668 \\
5) & 22.2544 \\
6) & 2438.00 \\
7) & 0.051042 \\
8) & 361.86 \\
9) & 0.21736 \\
\end{array}
}
\]