Multiplying decimals by powers of 10 worksheet for Grade 6 students.

Problem: Solving the worksheet on multiplying decimals by powers of 10

The task involves finding the missing numbers in each equation. The key concept here is understanding how multiplying by powers of 10 affects decimal numbers. When you multiply a number by a power of 10, the decimal point moves to the right by the number of zeros in that power.

Let's solve each problem step by step:

---

#### 1) \( 10000 \times \_\_\_\_\_\_ = 20970 \)

- Here, we need to find a number that, when multiplied by 10,000, gives 20,970.
- To find this, divide 20,970 by 10,000:
\[
\frac{20970}{10000} = 2.097
\]
- Therefore, the missing number is \( 2.097 \).

Answer: \( 2.097 \)

---

#### 2) \( 2.790 \times \_\_\_\_\_\_ = 2790 \)

- Here, we need to find a number that, when multiplied by 2.790, gives 2,790.
- To find this, divide 2,790 by 2.790:
\[
\frac{2790}{2.790} = 1000
\]
- Therefore, the missing number is \( 1000 \).

Answer: \( 1000 \)

---

#### 3) \( 10000 \times \_\_\_\_\_\_ = 14282 \)

- Here, we need to find a number that, when multiplied by 10,000, gives 14,282.
- To find this, divide 14,282 by 10,000:
\[
\frac{14282}{10000} = 1.4282
\]
- Therefore, the missing number is \( 1.4282 \).

Answer: \( 1.4282 \)

---

#### 4) \( 2.4 \times \_\_\_\_\_\_ = 24000 \)

- Here, we need to find a number that, when multiplied by 2.4, gives 24,000.
- To find this, divide 24,000 by 2.4:
\[
\frac{24000}{2.4} = 10000
\]
- Therefore, the missing number is \( 10000 \).

Answer: \( 10000 \)

---

#### 5) \( 100 \times \_\_\_\_\_\_ = 277.4546 \)

- Here, we need to find a number that, when multiplied by 100, gives 277.4546.
- To find this, divide 277.4546 by 100:
\[
\frac{277.4546}{100} = 2.774546
\]
- Therefore, the missing number is \( 2.774546 \).

Answer: \( 2.774546 \)

---

#### 6) \( 3.172 \times \_\_\_\_\_\_ = 31.72 \)

- Here, we need to find a number that, when multiplied by 3.172, gives 31.72.
- To find this, divide 31.72 by 3.172:
\[
\frac{31.72}{3.172} = 10
\]
- Therefore, the missing number is \( 10 \).

Answer: \( 10 \)

---

#### 7) \( \_\_\_\_\_\_ \times 1000 = 2001.41 \)

- Here, we need to find a number that, when multiplied by 1,000, gives 2,001.41.
- To find this, divide 2,001.41 by 1,000:
\[
\frac{2001.41}{1000} = 2.00141
\]
- Therefore, the missing number is \( 2.00141 \).

Answer: \( 2.00141 \)

---

#### 8) \( 2.696 \times \_\_\_\_\_\_ = 2696 \)

- Here, we need to find a number that, when multiplied by 2.696, gives 2,696.
- To find this, divide 2,696 by 2.696:
\[
\frac{2696}{2.696} = 1000
\]
- Therefore, the missing number is \( 1000 \).

Answer: \( 1000 \)

---

#### 9) \( 3.900 \times \_\_\_\_\_\_ = 390 \)

- Here, we need to find a number that, when multiplied by 3.900, gives 390.
- To find this, divide 390 by 3.900:
\[
\frac{390}{3.900} = 100
\]
- Therefore, the missing number is \( 100 \).

Answer: \( 100 \)

---

#### 10) \( \_\_\_\_\_\_ \times 3.0 = 30 \)

- Here, we need to find a number that, when multiplied by 3.0, gives 30.
- To find this, divide 30 by 3.0:
\[
\frac{30}{3.0} = 10
\]
- Therefore, the missing number is \( 10 \).

Answer: \( 10 \)

---

Final Answers:

\[
\boxed{
\begin{array}{ll}
1) & 2.097 \\
2) & 1000 \\
3) & 1.4282 \\
4) & 10000 \\
5) & 2.774546 \\
6) & 10 \\
7) & 2.00141 \\
8) & 1000 \\
9) & 100 \\
10) & 10 \\
\end{array}
}
\]