Adding And Subtracting In Scientific Notation

🔑 Key Concepts

  • To add or subtract numbers in scientific notation, the powers of 10 must match first.
  • This is similar to combining like terms: \( 3x^2 + 4x^2 = 7x^2 \), but \( 3x^2 + 4x^3 \) cannot be combined directly.
  • When the exponents are different, rewrite one number using an equivalent power of 10.
  • After the exponents match, add or subtract the coefficients.
  • Finish by rewriting the answer in proper scientific notation, with a coefficient from 1 up to 10.

✏️ Worked Examples

🧠 Math Vocabulary

  • Scientific notation: A way to write very large or very small numbers using a coefficient and a power of 10.
  • Coefficient: The decimal factor in front of the power of 10. In \( 6.4 \times 10^2 \), the coefficient is \( 6.4 \).
  • Power of 10: An expression such as \( 10^2 \), \( 10^{-3} \), or \( 10^5 \).
  • Exponent: The number that tells how many places the decimal moves when multiplying by a power of 10.
  • Like terms: Terms that have the same variable part or same power. Scientific notation terms can be combined directly only when the powers of 10 match.
  • Equivalent scientific notation: Rewriting a number with a different coefficient and exponent while keeping the same value, such as \( 3 \times 10^1 = 0.3 \times 10^2 \).
  • Normalize: Adjust the final answer so the coefficient is at least 1 and less than 10.

💡 Main Idea

When adding or subtracting in scientific notation, the powers of 10 must match before the coefficients can be combined. This works like combining like terms: the base and exponent must be the same before you add or subtract the front numbers.

📚 What You Should Already Know

Students should know how to write numbers in scientific notation, convert between scientific notation and standard form, and understand how positive and negative powers of 10 move the decimal point.

🚀 What Comes Next

After practicing addition and subtraction, students can extend their scientific notation skills to multiplication, division, and real-world applications involving very large or very small quantities.

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