Scientific Notation Operations Worksheet

Name:

Date:

🔢 Part 1: Basic Operations with Scientific Notation

1. Multiply: (3.2 × 10⁴) × (2 × 10³)

2. Divide: (9 × 10⁵) ÷ (3 × 10²)

3. Add: 4.5 × 10⁶ + 2.3 × 10⁶

4. Subtract: 8.7 × 10⁻³ - 3.2 × 10⁻³

5. Add with different powers: 5.4 × 10⁷ + 3.2 × 10⁶

Hint: Convert to the same power of 10 first

🌌 Part 2: Real-World Applications

6. The distance from Earth to the Sun is approximately 1.5 × 10⁸ kilometres. Light travels at 3.0 × 10⁵ kilometres per second. How long does it take light to travel from the Sun to Earth?

Step 1: Write the formula: Time = Distance ÷ Speed

Step 2: Calculate and express your answer in scientific notation:

7. A red blood cell has a diameter of approximately 7.5 × 10⁻⁶ metres. A virus has a diameter of 2.5 × 10⁻⁸ metres. How many times larger is the red blood cell than the virus?

8. The mass of an electron is 9.11 × 10⁻³¹ kg. The mass of a proton is 1.67 × 10⁻²⁷ kg. What is the combined mass of one electron and one proton?

Estimation check: Before calculating, estimate whether your answer will be closer to 10⁻²⁷ or 10⁻³¹. Explain why.

Calculation:

📝 Part 3: Quick Assessment Quiz

9. Calculate: (4.2 × 10⁻⁵) × (3.0 × 10⁸)

1.26 × 10³

1.26 × 10⁴

12.6 × 10³

1.26 × 10¹³

10. Which calculation gives the most reasonable estimate for (7.8 × 10⁶) ÷ (1.9 × 10³)?

About 4 × 10²

About 4 × 10³

About 40 × 10³

About 4 × 10⁹

11. Explain the steps needed to add 3.4 × 10⁵ + 2.7 × 10⁴. Show your working.

12. Vocabulary Check: Fill in the blanks using these terms: coefficient, exponent, power of ten, estimation

In the number 6.2 × 10⁷, the _____________ is 6.2 and the _____________ is 7. The term 10⁷ represents a _____________. When checking if an answer is reasonable, we use _____________.