Question 1: Express 0.00045 in scientific notation.

Answer: 4.5 × 10⁻⁴

Question 2: Write the number 0.0000072 in standard form using scientific notation.

Answer: 7.2 × 10⁻⁶

Question 3: Convert 3.6 × 10⁻⁵ to decimal form.

Answer: 0.000036

Question 4: Identify the mistake in writing 2.5 × 10⁻³ as 25 × 10⁻⁴ and correct it.

Answer: The mistake is that 2.5 × 10⁻³ is not equal to 25 × 10⁻⁴; the correct form is 2.5 × 10⁻³, or 2.5e-3.

Question 5: Plot the point representing 5.4 × 10⁻⁴ on the number line provided in the grid.

Answer: Student plots at 0.00054 (just left of 0.001).

Question 6: A scientist measures a small sample of a substance as 0.0000032 grams. Express this in scientific notation.

Answer: 3.2 × 10⁻⁶

Question 7: If a small number is written as 6.7 × 10⁻⁵, what is its decimal equivalent?

Answer: 0.000067

Question 8: A new particle has a mass of 0.000000045 kg. Write its mass in scientific notation.

Answer: 4.5 × 10⁻⁸

Question 9: Construct a small triangle on the grid with side lengths 2.5 × 10⁻², 3.0 × 10⁻², and 4.5 × 10⁻² meters. Show your steps.

Answer: Student draws and labels triangle with approximate lengths in grid units.

Question 10: Express 0.000000123 in scientific notation.

Answer: 1.23 × 10⁻⁷

Question 11: Identify and correct the error: writing 9.8 × 10⁻⁴ as 98 × 10⁻⁶.

Answer: The correct form of 9.8 × 10⁻⁴ is 9.8 × 10⁻⁴; the error was misplacing the decimal point and the exponent.