Order of Magnitude

Summary

• A number in scientific notation has the form…

  a × 10ⁿ

  where…

  a	is a decimal number called the mantissa
  n	is an integer called the order, index, exponent, or power

• Scientific notation is a method for writing numbers that…
  • is useful for writing numbers that are too large or too small to write conveniently in decimal form
  • simplifies some mental calculations
• There are two conventions for writing numbers in scientific notation.
  standard form

  0 < a < 10

  • The mantissa has a single non-zero digit before the decimal point.
  • Significant digits are isolated from the placeholder digits

  engineering notation

  n = 0, ±3, ±6, ±9, …

  • The order is an integer multiple of 3.
  • Determining SI prefixes is made easier. 
• Order of magnitude
  • An order of magnitude change is an increase or decrease by a power of 10.
  • Estimation should lead to values that are within an order of magnitude of their actual value.