Math Skills Review: Scientific Notation

Introduction to Scientific Notation

• Purpose: Simplifies handling very large or very small numbers.
• Format: Composed of a digit term and an exponential term.
  • Example: 5.6 x 10⁻⁹, where 5.6 is the digit term and 10⁻⁹ is the exponential term.

Examples of Scientific Notation

• Positive Numbers:
  • 10,000 = 1 x 10⁴
  • 1,000 = 1 x 10³
  • 100 = 1 x 10²
• Negative Exponents:
  • 0.1 = 1 x 10⁻¹
  • 0.01 = 1 x 10⁻²
  • 0.001 = 1 x 10⁻³

Interpreting Scientific Notation

• Exponent of 10:
  • Positive: Decimal point is shifted to the right.
  • Negative: Decimal point is shifted to the left.
• Significant Figures:
  • Digit term indicates the number of significant figures.

Calculations with Scientific Notation

Using a Scientific Calculator

• Enter the digit term.
• Press EE or EXP button for exponent entry.
• Treat the number normally in calculations.
• Example Check: 6.0 x 10⁵ * 4.0 x 10³ = 2.4 x 10⁹.

Using a Non-Scientific Calculator

• Familiarity with exponents is required.

Addition and Subtraction

• Convert all numbers to the same power of 10 before adding or subtracting.
• Example:
  • (4.215 x 10⁻²) + (3.2 x 10⁻⁴) = 4.247 x 10⁻²

Multiplication

• Multiply digit terms and add exponents.
• Example:
  • (3.4 x 10⁶) * (4.2 x 10³) = 1.4 x 10¹⁰

Division

• Divide digit terms and subtract exponents.
• Example:
  • (6.4 x 10⁶) / (8.9 x 10²) = 7.2 x 10³

Powers of Exponentials

• Raise the digit term to the power and multiply the exponent by the power.
• Example:
  • (2.4 x 10⁴)³ = 1.4 x 10¹³

Roots of Exponentials

• Adjust the exponent to be divisible by the root.
• Example Answer: 4.2 x 10⁻³

Quiz

1. Write 0.000467 and 32,000,000 in scientific notation.
   • Answers: 4.67 x 10⁻⁴, 3.2 x 10⁷
2. Express 5.43 x 10⁻³ as a number.
   • Answer: 0.00543
3. Calculate (4.5 x 10⁻¹⁴) x (5.2 x 10³).
   • Answer: 2.3 x 10⁻¹⁰
4. Calculate (6.1 x 10⁵) / (1.2 x 10⁻³).
   • Answer: 5.1 x 10⁸
5. Solve (3.74 x 10⁻³)⁴.
   • Answer: 1.96 x 10⁻¹⁰
6. Find the fifth root of 7.20 x 10²².
   • Answer: 3.73 x 10⁴

Next Topics

• Algebraic Manipulation
• Significant Figures
• Manipulation of Exponents
• Dimensional Analysis
• Logarithms
• The Quadratic Equation