Question 1: Calculate: (3.2 × 10^5) + (4.7 × 10^4). Provide your answer in standard form.

Answer: 3.67 × 10^5

Question 2: Subtract: (6.5 × 10^6) - (2.3 × 10^6). Express the result in standard form.

Answer: 4.2 × 10^6

Question 3: A scientist records a value of 7.8 × 10^4 in an experiment. Another measurement is 2.95 × 10^4. Find the total in standard form.

Answer: 1.075 × 10^5

Question 4: A large sum of money is represented as 9.45 × 10^7 in one account and 4.2 × 10^7 in another. Find the combined total.

Answer: 1.365 × 10^8

Question 5: Add: (1.25 × 10^3) + (3.75 × 10^2). Write the answer in standard form.

Answer: 1.625 × 10^3

Question 6: Subtract: (8.9 × 10^4) - (2.3 × 10^4). Express the result in standard form.

Answer: 6.6 × 10^4

Question 7: A lab measures a value of 5.6 × 10^5 and then records a decrease of 1.2 × 10^5. What is the new value in standard form?

Answer: 4.4 × 10^5

Question 8: Combine: (2.5 × 10^6) + (3.75 × 10^6). Write the answer in standard form.

Answer: 6.25 × 10^6

Question 9: A store records a stock count of 4.2 × 10^4 units. If 1.8 × 10^4 units are added, what is the total stock in standard form?

Answer: 6.0 × 10^4

Question 10: Error Analysis: Students often confuse the addition of 3.4 × 10^5 and 4.7 × 10^4, mistakenly writing the sum as 3.87 × 10^5. Identify and correct the mistake.

Answer: The correct sum is 3.87 × 10^5, but since 4.7 × 10^4 = 0.47 × 10^5, the proper addition is (3.4 + 0.47) × 10^5 = 3.87 × 10^5. The mistake was in not converting the second number to the same power of ten before adding.

Question 11: Challenge & Extension: A researcher records two measurements: 1.05 × 10^8 and 2.35 × 10^8. Find their sum, expressed in standard form.

Answer: 3.40 × 10^8

Question 12: Mixed Review: Calculate: (7.6 × 10^3) - (2.45 × 10^3). Write your answer in standard form.

Answer: 5.15 × 10^3