converting scientific notation to standard notation

Changing Numbers from Scientific Notation to Standard Notation

  • Definition of Scientific Notation

    • A way of expressing numbers that are too large or too small using powers of ten.

    • Format: (aimes10n)(a imes 10^n) where

    • a = coefficient (a number between 1 and 10)

    • n = exponent (indicates the number of times 10 is multiplied by itself)

  • Process of Conversion

    • Positive Exponent

    • When the exponent is positive, the number is larger than 1.

    • This can be visualized as multiplying the coefficient by 10 for the number of times indicated by the exponent.

    • This operation can also be interpreted as moving the decimal point to the right.

    • Example: Converting (9.04imes107)(9.04 imes 10^7) to Standard Notation

    • Move the decimal point 7 places to the right.

    • Alternatively, multiply the coefficient (9.04) by 10, seven times.

    • When moving the decimal point right, add zeros as necessary to fill in empty spaces.

    • Conversion Result:

      • (9.04imes107=90,400,000)(9.04 imes 10^7 = 90,400,000)

  • Visual Representation and Multiplication

    • A graphic is referenced that visually displays the multiplication process of moving the decimal point each time you multiply by 10.

    • This graphic illustrates the incremental changes and reinforces the understanding of why moving the decimal point yields the equivalent result.