Question 1: Write the number 7,560,000 in scientific notation.

Answer: 7.56 × 10^6

Question 2: Express the number 0.000045 in scientific notation.

Answer: 4.5 × 10^-5

Question 3: Convert 3.2 × 10^8 into its decimal form.

Answer: 320,000,000

Question 4: Identify the error in this scientific notation: 9.4 × 10^−3 is written as 9.4 × 10^3.

Answer: The exponent sign is wrong; it should be negative, as 9.4 × 10^−3.

Question 5: A factory produces 5.2 × 10^7 units of product annually. How many units does it produce in standard decimal form?

Answer: 52,000,000

Question 6: Plot the graph of y = 2 × 10^x for x = -2 to 2 on the grid.

Answer: Values: y= 2 × 10^-2, 2 × 10^-1, 2 × 10^0, 2 × 10^1, 2 × 10^2.

Question 7: Construct a triangle with side lengths of 3 × 10^3 cm, 4 × 10^3 cm, and 5 × 10^3 cm. Calculate the perimeter in scientific notation.

Answer: 1.2 × 10^4 cm

Question 8: If a city’s population is 8.9 × 10^6, and it increases by 5% annually, what will be the population after one year? Express your answer in scientific notation.

Answer: 9.345 × 10^6

Question 9: A scientist records a measurement as 6.02 × 10^22 molecules. What is the number in standard decimal form?

Answer: 602,000,000,000,000,000,000,000

Question 10: Identify and correct the mistake in converting 2.5 × 10^3 to 2500.

Answer: No mistake; 2.5 × 10^3 = 2500. Correctly converted.

Question 11: Explain why scientific notation is useful when dealing with very large numbers.

Answer: Scientific notation simplifies calculations, makes large numbers easier to read and compare, and reduces errors in handling very big quantities.