Scientific notation

  1. Scientific notation is a means of succinctly expressing both small & large numbers.
    • A number expressed in scientific notation is in the form <coefficient> x <base><exponent>.
    • The coefficient is always a positive decimal number whose value is greater than or equal to 1 and less than 10, the base’s value is always 10 and the exponent can be any positive or negative integer.
    • To change a number from being expressed in scientific notation to being expressed as a decimal, its coefficient’s decimal point is moved left if the exponent is negative, and right if it’s positive. In both cases it’s moved by the number of digits equal to the absolute value of the exponent. Finally, the base and exponent are discarded.
    • A number expressed in scientific notation whose exponent is positive will always be greater than its coefficient, one whose exponent is negative will always be smaller than its coefficient, and one whose exponent is zero (0) will equal its coefficient.
  2. These examples show how to convert a number from being expressed in scientific notation to being expressed in the decimal number system.
    • They show numbers expressed in scientific notation which are greater, lesser & equal in value to their coefficients.
  3. Number in scientific notationCoefficientBaseExponentDirection to move decimal pointNumber as a decimal
    1.23 x 1041.23104Right12300
    1.23 x 10-41.2310-4Left0.000123
    1.23 x 1001.23100None1.23