Question 1: Express the number 0.005 in scientific notation.

Answer: 5 × 10⁻³

Question 2: Write 0.00076 in standard form using scientific notation.

Answer: 7.6 × 10⁻⁴

Question 3: Calculate the value of (3 × 10⁻⁴) × (2 × 10⁻³).

Answer: 6 × 10⁻⁷

Question 4: A small bacterial count is 0.00000045 grams. Express this in scientific notation.

Answer: 4.5 × 10⁻⁷

Question 5: Identify and correct the mistake: Write 0.00012 as 1.2 × 10⁻⁴.

Answer: The correct scientific notation should be 1.2 × 10⁻⁴, so the mistake is in the exponent; it should be 10⁻⁴, not 10⁻⁵.

Question 6: Construct a small number between 0.001 and 0.01 in scientific notation.

Answer: 5 × 10⁻³

Question 7: A scientist records a tiny measurement as 3.2 × 10⁻⁵ grams. What is the decimal form?

Answer: 0.000032

Question 8: Explain why writing 0.00056 as 5.6 × 10⁻⁴ is correct or incorrect.

Answer: It's correct because 0.00056 = 5.6 × 10⁻⁴; the decimal point moves 4 places to the right.

Question 9: Plot the point representing 2.5 × 10⁻⁴ on the number line in the grid provided.

Answer: Students should locate 0.00025 on the number line.

Question 10: A lab needs to measure a solution as 0.0000032 liters. Write this in scientific notation.

Answer: 3.2 × 10⁻⁶

Question 11: Identify the common misconception in the following statement: '0.045 in scientific notation is 4.5 × 10⁻³ because the decimal moves 3 places.'

Answer: Incorrect; it should be 4.5 × 10⁻² because the decimal moves 2 places.

Question 12: Challenge: Write 0.000000123 in scientific notation and explain your steps.

Answer: It is 1.23 × 10⁻⁷; move the decimal 7 places to the right to get from 0.000000123 to 1.23.