Question 1: Calculate the sum of 3.2 × 10^4 and 5.8 × 10^3. Express your answer in standard form.

Answer: 3.78 × 10^4

Question 2: Subtract 4.5 × 10^5 from 7.2 × 10^5. Write the result in standard form.

Answer: 2.7 × 10^5

Question 3: Add 1.5 × 10^6 and 2.3 × 10^5. Show your working and give the answer in standard form.

Answer: 1.73 × 10^6

Question 4: A bridge construction project requires 2.4 × 10^7 kg of steel. If 1.2 × 10^7 kg has already been delivered, how much steel is still needed? Express your answer in standard form.

Answer: 1.2 × 10^7

Question 5: An engineer measures the length of a beam as 5.2 × 10^2 mm. After adjustments, the length is reduced by 1.3 × 10^2 mm. What is the new length? Express in standard form.

Answer: 3.9 × 10^2

Question 6: Calculate 6.75 × 10^3 + 2.5 × 10^4, expressed in standard form.

Answer: 3.175 × 10^4

Question 7: A turbine generates power at 1.2 × 10^9 Watts. Due to maintenance, its output drops by 3.5 × 10^8 Watts. What is the new power output? Write your answer in standard form.

Answer: 8.5 × 10^8

Question 8: Construct a line segment on the grid that represents a length of 4.7 × 10^3 units. Then, extend it by subtracting 1.2 × 10^3 units. What is the total length?

Answer: 3.5 × 10^3

Question 9: Subtract 8.9 × 10^4 from 1.2 × 10^5. Give your answer in standard form.

Answer: 3.1 × 10^4

Question 10: An engineer needs to combine two components with masses 2.3 × 10^6 kg and 1.7 × 10^6 kg. Find the total mass.

Answer: 4.0 × 10^6

Question 11: A factory produces 5.2 × 10^4 units of a product daily. Due to a defect, 2.8 × 10^4 units are discarded. How many units are good? Express in standard form.

Answer: 2.4 × 10^4

Question 12: Identify and correct the mistake: Subtracting 3.4 × 10^5 from 2.1 × 10^6 gives 1.76 × 10^6.

Answer: Correct answer is 1.76 × 10^6; mistake is in initial subtraction or misalignment of exponents.