Question 1: Calculate: (3 × 10^4) × (2 × 10^3).

Answer: 6 × 10^7

Question 2: Divide: (8 × 10^6) ÷ (2 × 10^2).

Answer: 4 × 10^4

Question 3: Express the calculation 7.5 × 10^3 ÷ 3 × 10^2 in standard form.

Answer: 2.5 × 10^1

Question 4: A scientist has a sample of a substance weighing 4.2 × 10^5 grams. If they divide the sample into 7 × 10^4 equal parts, what is the weight of each part?

Answer: 6 grams

Question 5: Calculate: (2.5 × 10^6) ÷ (5 × 10^2).

Answer: 5 × 10^3

Question 6: A factory produces 3.2 × 10^4 items each day. How many items are produced in 15 days?

Answer: 4.8 × 10^5

Question 7: Calculate: (9 × 10^3) × (4 × 10^2).

Answer: 3.6 × 10^6

Question 8: A vehicle travels at a speed of 2.5 × 10^2 km/h. How far will it travel in 3 × 10^1 hours?

Answer: 7.5 × 10^3 km

Question 9: Express the calculation (1.2 × 10^5) ÷ (4 × 10^2) in standard form.

Answer: 3 × 10^2

Question 10: A researcher records a bacteria count of 5.6 × 10^3 in a sample. If they dilute the sample by a factor of 10^2, what is the new bacteria count?

Answer: 5.6 × 10^1

Question 11: Calculate: (6 × 10^4) ÷ (3 × 10^2).

Answer: 2 × 10^2

Question 12: Identify and correct the mistake in this calculation: (4 × 10^5) ÷ (2 × 10^3) = 2 × 10^2.

Answer: Correct answer is 2 × 10^2, but the mistake is in the calculation. The student incorrectly simplified, but the initial calculation is correct.