Let's solve each problem step by step. The goal is to
find the missing number in each multiplication equation involving decimals and powers of 10.
---
🔹 Key Concept:
When you multiply a decimal by a power of 10 (like 10, 100, 1000, etc.), you move the
decimal point to the right by the number of zeros in the power of 10.
For example:
- $ 3.45 \times 10 = 34.5 $ → move decimal 1 place right
- $ 3.45 \times 100 = 345 $ → move decimal 2 places right
Conversely, if we know the result and want to find the original number, we can reverse this process:
move the decimal point to the left.
---
Now let’s solve each one:
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####
1) $ 10000 \times \_\_\_\_\_\_\_\_ = 20970 $
We need to divide 20970 by 10000:
$$
\frac{20970}{10000} = 2.097
$$
✔ Answer: 2.097
---
####
2) $ 2.790 \times \_\_\_\_\_\_\_\_ = 2790 $
We divide 2790 by 2.790:
$$
\frac{2790}{2.790} = 1000
$$
✔ Answer: 1000
> Note: Moving decimal 3 places right turns 2.790 → 2790, so multiplier is $ 10^3 = 1000 $
---
####
3) $ 10000 \times \_\_\_\_\_\_\_\_ = 14282 $
Divide:
$$
\frac{14282}{10000} = 1.4282
$$
✔ Answer: 1.4282
---
####
4) $ 2.4 \times \_\_\_\_\_\_\_\_ = 24000 $
Divide:
$$
\frac{24000}{2.4} = 10000
$$
✔ Answer: 10000
> Because 2.4 × 10000 = 24000
---
####
5) $ 100 \times \_\_\_\_\_\_\_\_ = 277.4546 $
Divide:
$$
\frac{277.4546}{100} = 2.774546
$$
✔ Answer: 2.774546
---
####
6) $ 3.172 \times \_\_\_\_\_\_\_\_ = 31.72 $
Divide:
$$
\frac{31.72}{3.172} = 10
$$
✔ Answer: 10
> Move decimal 1 place right → ×10
---
####
7) $ \_\_\_\_\_\_\_\_ \times 1000 = 2001.41 $
Divide:
$$
\frac{2001.41}{1000} = 2.00141
$$
✔ Answer: 2.00141
---
####
8) $ 2.696 \times \_\_\_\_\_\_\_\_ = 2696 $
Divide:
$$
\frac{2696}{2.696} = 1000
$$
✔ Answer: 1000
> 2.696 → 2696 = move decimal 3 places → ×1000
---
####
9) $ 3.900 \times \_\_\_\_\_\_\_\_ = 390 $
Divide:
$$
\frac{390}{3.900} = 100
$$
✔ Answer: 100
> 3.900 × 100 = 390
---
####
10) $ \_\_\_\_\_\_\_\_ \times 3.0 = 30 $
Divide:
$$
\frac{30}{3.0} = 10
$$
✔ Answer: 10
---
✔ Final Answers:
1.
2.097
2.
1000
3.
1.4282
4.
10000
5.
2.774546
6.
10
7.
2.00141
8.
1000
9.
100
10.
10
---
📌 Summary Tip:
To find the missing factor when multiplying by a power of 10:
- If the known number is
smaller than the result → multiply by a power of 10
- If the known number is
larger → divide to find the missing factor
Use
division to reverse the multiplication.
Let me know if you'd like this as a printable answer sheet!
Parent Tip: Review the logic above to help your child master the concept of multiplying decimals worksheet 6th grade.
