Standard Form Multiplication

Name:

Date:

Scientific notation and mathematical symbols

📚 Part 1: Basic Multiplication

Remember: Multiply coefficients, add powers of 10, then check your coefficient is between 1 and 10.

1. (3 × 10⁴) × (2 × 10³) = _______________

2. (5 × 10²) × (4 × 10⁵) = _______________

3. (7 × 10⁻¹) × (3 × 10⁴) = _______________

4. (2.5 × 10³) × (1.2 × 10⁴) = _______________

5. Which of the following shows the correct method for multiplying (6 × 10²) × (8 × 10³)?

14 × 10⁵

48 × 10⁵ = 4.8 × 10⁶

6 × 8 × 10² × 10³ = 48 × 10⁶

(6 + 8) × 10⁽²⁺³⁾ = 14 × 10⁵

🔬 Part 2: Real-World Applications

6. The mass of one hydrogen atom is 1.7 × 10⁻²⁷ kg. The mass of one oxygen atom is 2.7 × 10⁻²⁶ kg. Calculate the total mass when you have 1000 hydrogen atoms and 500 oxygen atoms.

Step 1: Mass of 1000 hydrogen atoms = (1.7 × 10⁻²⁷) × (1.0 × 10³) = _______________

Step 2: Mass of 500 oxygen atoms = (2.7 × 10⁻²⁶) × (5.0 × 10²) = _______________

7. The distance from Earth to the nearest star (Proxima Centauri) is 4.0 × 10¹³ km. Light travels at 3.0 × 10⁵ km per second. How far does light travel in one day? (1 day = 8.64 × 10⁴ seconds)

8. A scientist needs to calculate the area of a rectangular cell membrane. The length is 6.5 × 10⁻⁶ metres and the width is 3.2 × 10⁻⁷ metres. What is the area in square metres?

🎯 Part 3: Challenge Questions

9. Calculate: (4 × 10³) × (5 × 10⁻²) × (2 × 10⁴)

10. A computer processes 2.4 × 10⁹ calculations per second. In one hour (3.6 × 10³ seconds), it performs a certain number of calculations. If each calculation uses 1.5 × 10⁻¹² joules of energy, what is the total energy used in one hour?

11. Explain in your own words why we add the powers when multiplying numbers in standard form, rather than multiplying them.