Which product has 4 zeros after the digit 3? 0.3 \times 10^4 0.03 \times 10^4 0.3 \times 10^5 0.03 \times 10^5
The correct Answer and Explanation is:
Correct Answer:
0.3 × 10⁵
Explanation:
To find the product that has four zeros after the digit 3, we must evaluate each expression by performing the multiplication and then observing the resulting number.
Let’s evaluate each option step-by-step:
1. 0.3 × 10⁴
10⁴ = 10,000
⇒ 0.3 × 10,000 = 3,000
This gives three zeros after the digit 3, not four.
✗ Not the correct answer
2. 0.03 × 10⁴
10⁴ = 10,000
⇒ 0.03 × 10,000 = 300
This gives two zeros after the digit 3.
✗ Not the correct answer
3. 0.3 × 10⁵
10⁵ = 100,000
⇒ 0.3 × 100,000 = 30,000
This gives four zeros after the digit 3.
✓ ✅ This is the correct answer
4. 0.03 × 10⁵
10⁵ = 100,000
⇒ 0.03 × 100,000 = 3,000
This gives three zeros after the digit 3.
✗ Not the correct answer
Why the Answer Is 0.3 × 10⁵:
Multiplying by powers of 10 moves the decimal point to the right. The number of places you move the decimal equals the exponent on 10. In this case:
- 0.3 means “3 tenths” or 3/10.
- Multiplying by 10⁵ (100,000) moves the decimal point 5 places to the right:
0.3 × 10⁵ = 30,000 - The result is 30,000, which has a digit 3 followed by four zeros.
This is exactly what the question asked for.
Therefore, 0.3 × 10⁵ is the only product that produces a number with four zeros after the digit 3.
