Scientific Notation Basics

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📚 Part 1: Understanding Scientific Notation

1. Scientific notation is written as a coefficient × 10 raised to an exponent. Which of these shows correct scientific notation?

12.5 × 10³

1.25 × 10⁴

0.125 × 10⁵

125 × 10²

2. The distance from Earth to the Sun is approximately 150,000,000 km. In scientific notation, this is:

1.5 × 10⁷ km

1.5 × 10⁸ km

15 × 10⁷ km

1.5 × 10⁹ km

3. The size of an atom is approximately 1 × 10⁻¹⁰ metres. In standard decimal form, this is:

0.000000001 m

0.0000000001 m

0.00000000001 m

0.000000000001 m

4. Which number is the largest?

3.2 × 10⁵

5.1 × 10⁴

2.9 × 10⁶

7.8 × 10⁵

✏️ Part 2: Converting Numbers

5. Convert these numbers to scientific notation:

a) 45,000 = ________________

b) 0.0072 = ________________

c) 890,000,000 = ________________

d) 0.000034 = ________________

6. Convert these numbers from scientific notation to standard decimal form:

a) 6.7 × 10³ = ________________

b) 2.4 × 10⁻⁴ = ________________

c) 9.15 × 10⁶ = ________________

d) 8.2 × 10⁻² = ________________

7. Order these numbers from smallest to largest:

7.35 × 10⁻³, 0.008, 5.2 × 10⁻², 0.0012

8. Explain in your own words what the exponent tells us in scientific notation:

🌍 Part 3: Real-World Applications

9. New Zealand's population is approximately 5,200,000 people. Write this in scientific notation and explain why scientific notation might be useful for comparing populations of different countries.

Scientific notation: ________________

10. A red blood cell has a diameter of about 0.000007 metres. Write this in scientific notation and calculate how many times larger a 1-centimetre object is compared to a red blood cell.

Red blood cell diameter: ________________