Standard Form Small Numbers

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Date:

📚 Part 1: Converting to Standard Form

Remember: Standard form is written as a × 10ⁿ where 1 ≤ a < 10

1. Write these decimal numbers in standard form:

a) 0.006 = _____________ × 10_____

b) 0.0072 = _____________ × 10_____

c) 0.000045 = _____________ × 10_____

d) 0.5 = _____________ × 10_____

2. The thickness of a human hair is 0.000075 metres. Write this in standard form:

3. A red blood cell has a diameter of 0.0000075 metres. Express this measurement in standard form:

✏️ Part 2: Converting from Standard Form

4. Write these numbers in decimal form:

a) 4.2 × 10⁻³ = _____________

b) 7.5 × 10⁻⁵ = _____________

c) 1.8 × 10⁻² = _____________

d) 9.6 × 10⁻⁴ = _____________

5. Which of these numbers is written correctly in standard form?

0.5 × 10⁻³

5.0 × 10⁻⁴

15 × 10⁻²

1.5 × 10⁻¹

6. Order these numbers from smallest to largest:

3.2 × 10⁻⁴, 7.1 × 10⁻³, 2.5 × 10⁻⁵, 8.9 × 10⁻³

Smallest: _____________ → _____________ → _____________ → _____________ :Largest

🔬 Part 3: Problem Solving

7. A bacteria cell measures 2.5 × 10⁻⁶ metres in length. How would you write this measurement in decimal form, and what does this tell you about the size of bacteria?

8. Explain why standard form is useful when working with very small numbers. Give one real-world example where this would be helpful:

9. Challenge: If the width of a DNA strand is approximately 2.5 × 10⁻⁹ metres, and the thickness of a sheet of paper is 1.0 × 10⁻⁴ metres, how many times thicker is the paper than the DNA strand?