Question 1: Calculate (3.2 × 10^4) + (4.7 × 10^3).

Answer: 3.67 × 10^4

Question 2: Subtract (6.5 × 10^5) - (2.3 × 10^5).

Answer: 4.2 × 10^5

Question 3: Add (1.2 × 10^6) + (3.4 × 10^5).

Answer: 1.54 × 10^6

Question 4: Calculate (7.8 × 10^3) - (3.2 × 10^3).

Answer: 4.6 × 10^3

Question 1: A scientist measures a value as (6.4 × 10^5). Another measurement is (2.5 × 10^5). When combining these measurements, what is the total? Explain your process.

Answer: Total is 8.9 × 10^5 by adding the coefficients 6.4 + 2.5 = 8.9, keeping the same power of 10^5.

Question 2: A construction project requires (4.3 × 10^4) bricks. If 1.2 × 10^4 bricks are used, how many bricks remain? Provide your working.

Answer: Remaining bricks = 4.3 × 10^4 - 1.2 × 10^4 = (4.3 - 1.2) × 10^4 = 3.1 × 10^4

Question 1: A car's speed is 2.5 × 10^2 km/h. Its speed increases by 4.5 × 10^1 km/h. What is its new speed?

Answer: New speed = 2.5 × 10^2 + 4.5 × 10^1 = (250 + 45) km/h = 295 km/h

Question 2: A bacteria culture has a population of (3.2 × 10^6). After some time, the population decreases by (1.1 × 10^6). What is the new population?

Answer: New population = 3.2 × 10^6 - 1.1 × 10^6 = (3.2 - 1.1) × 10^6 = 2.1 × 10^6

Question 1: Calculate (8.6 × 10^7) + (2.4 × 10^8).

Answer: Sum is (0.86 + 2.4) × 10^8 = 3.26 × 10^8

Question 2: Subtract (5.7 × 10^9) - (3.9 × 10^8).

Answer: Difference = (5.7 × 10^9) - (0.39 × 10^9) = (5.7 - 0.39) × 10^9 = 5.31 × 10^9

Question 1: A student calculates: (3.4 × 10^5) + (2.1 × 10^5) = 5.5 × 10^5. Is this correct? If not, explain and correct the mistake.

Answer: Incorrect. The correct sum is 3.4 + 2.1 = 5.5, so the answer is 5.5 × 10^5. The calculation is correct; no mistake if calculation is accurate.

Question 2: A student subtracts: (7.8 × 10^4) - (4.2 × 10^3) = 3.6 × 10^4. Identify the error and provide the correct answer.

Answer: Error: Coefficients are not in the same power of ten. Correct calculation: 7.8 × 10^4 - 0.42 × 10^4 = (7.8 - 0.42) × 10^4 = 7.38 × 10^4