Math foundation notes-scinctic notation 1A

Scientific Notation Fundamentals

• Format of Scientific Notation

  • Whole number must be > 1 and < 10, or = 1.

  • The exponent can vary and must be an integer.

  • Negative Numbers: Represented with a small exponent (e.g., less than 1).

  • Big Numbers: Represented with a positive exponent.

Moving the Decimal

• To adjust the exponent:

  • Move decimal left: This indicates a positive exponent.

  • Move decimal right: This indicates a negative exponent.

Multiplying in Scientific Notation

• Always involves multiplying by powers of ten.

• Examples of conversion:

  • Example: 530,000 = 5.3 x 10^5

  • Example: .00078 = 7.8 x 10^-4

  • Example: 3.8 x 10^3 implies 3.8 equals 3.8 multiplied by 1000 (10^3).

  • Example: 2.8 x 10^6 implies moving the decimal six places to the right: 2,800,000.

  • Example: 43 = 4.3 x 10^1

  • Example: 0.00045 = 4.5 x 10^-4.

Key Reminders

• The standard form must always be in the structure x x 10^n.

• The primary goal is to adjust numbers to ensure the first digit lies between 1 and 10, typically requiring manipulation of decimal placements.