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Study Guides > ALGEBRA / TRIG I

Summary: Scientific Notation

 

Key Concepts

  • Summary of Exponent Properties
    • If a,ba,b are real numbers and m,nm,n are integers, then Product Propertyaman=am+nPower Property(am)n=amnProduct to a Power Property(ab)m=ambmQuotient Propertyaman=amn,a0Zero Exponent Propertya0=1,a0Quotient to a Power Property(ab)m=ambm,b0Definition of Negative Exponentan=1an\begin{array}{cccc}\mathbf{\text{Product Property}}\hfill & & & {a}^{m}\cdot {a}^{n}={a}^{m+n}\hfill \\ \mathbf{\text{Power Property}}\hfill & & & {\left({a}^{m}\right)}^{n}={a}^{m\cdot n}\hfill \\ \mathbf{\text{Product to a Power Property}}\hfill & & & {\left(ab\right)}^{m}={a}^{m}{b}^{m}\hfill \\ \mathbf{\text{Quotient Property}}\hfill & & & {\Large\frac{{a}^{m}}{{a}^{n}}}={a}^{m-n},a\ne 0\hfill \\ \mathbf{\text{Zero Exponent Property}}\hfill & & & {a}^{0}=1,a\ne 0\hfill \\ \mathbf{\text{Quotient to a Power Property}}\hfill & & & {\left({\Large\frac{a}{b}}\right)}^{m}={\Large\frac{{a}^{m}}{{b}^{m}}},b\ne 0\hfill \\ \mathbf{\text{Definition of Negative Exponent}}\hfill & & & {a}^{-n}={\Large\frac{1}{{a}^{n}}}\hfill \end{array}
  • Convert from Decimal Notation to Scientific Notation: 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, nn , that the decimal point was moved.
    3. Write the number as a product with a power of 1010.
      • If the original number is greater than 11, the power of 1010 will be 10n{10}^{n} .
      • If the original number is between 00 and 11, the power of 1010 will be 10n{10}^{n} .
    4. Check.
  • Convert Scientific Notation to Decimal Form: To convert scientific notation to decimal form:
    1. Determine the exponent, nn , on the factor 1010.
    2. Move the decimal nn places, adding zeros if needed.
      • If the exponent is positive, move the decimal point nn places to the right.
      • If the exponent is negative, move the decimal point n|n| places to the left.
    3. Check.

Glossary

negative exponent
If nn is a positive integer and a0a\ne 0 , then an=1an{a}^{-n}=\frac{1}{{a}^{n}} .
scientific notation
A number expressed in the form a×10na\times {10}^{n}, where a1a\ge 1 and a<10a<10, and nn is an integer.
 

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