Mathematics » Polynomials II » Integer Exponents and Scientific Notation

Integer Exponents and Scientific Notation Summary

Key Concepts

  • Property of Negative Exponents
    • If \(n\) is a positive integer and \(a\ne 0\), then \(\frac{1}{{a}^{\text{−}n}}={a}^{n}\)
  • Quotient to a Negative Exponent
    • If \(a,b\) are real numbers, \(b\ne 0\) and \(n\) is an integer , then \({\left(\frac{a}{b}\right)}^{\text{−}n}={\left(\frac{b}{a}\right)}^{n}\)
  • To convert a decimal to scientific notation:
    1. Move the decimal point so that the first factor is greater than or equal to 1 but less than 10.
    2. Count the number of decimal places, \(n\), that the decimal point was moved.
    3. Write the number as a product with a power of 10. If the original number is:
      • greater than 1, the power of 10 will be \({10}^{n}\)
      • between 0 and 1, the power of 10 will be \({10}^{\text{−}n}\)
    4. Check.
  • To convert scientific notation to decimal form:
    1. Determine the exponent, \(n\), on the factor 10.
    2. Move the decimal \(n\)places, adding zeros if needed.
      • If the exponent is positive, move the decimal point \(n\) places to the right.
      • If the exponent is negative, move the decimal point \(|n|\) places to the left.
    3. Check.

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