Scientific Notation Tutorial

Introduction to Scientific Notation:

Scientific notation expresses very large or very small numbers in the form "a × 10^b", where "a" is between 1 and 10, and "b" is an integer.

Example: The speed of light is approximately 2.99792458 × 10^8 m/s.

Converting Numbers to Scientific Notation:

• Identify the coefficient "a" (1 ≤ a < 10).
• Count decimal places to move for a whole number.
• Positive exponent if number ≥ 1; negative if < 1.
• Write as "a × 10^b".

Example: 25,000 → 2.5 × 10^4

Converting Numbers from Scientific Notation:

• Identify "a" and exponent "b".
• Move decimal point b places right if b positive, left if negative.
• Add zeros as needed.

Example: 6.02 × 10^23 → 602,000,000,000,000,000,000,000

Operations with Scientific Notation:

Before addition or subtraction, exponents must match. Then combine coefficients.

Example: 3.5 × 10^4 + 2.1 × 10^3 → adjust 2.1 × 10^3 to 0.21 × 10^4 → 3.5 + 0.21 = 3.71 × 10^4

Example 1: Distance to Alpha Centauri

Alpha Centauri is ~4.37 × 10^13 km away. Convert to meters (1 km = 1000 m → ×10^3).

4.37 × 10^13 km × 10^3 = 4.37 × 10^16 m

Example 2: Avogadro's Number

Avogadro's number ≈ 6.022 × 10^23 atoms/mole. For 2 moles:

Number of atoms = 2 × 6.022 × 10^23 = 1.2044 × 10^24 atoms