In science and mathematics, we frequently deal with numbers that are either extremely large (like the speed of light: 299,792,458 m/s) or extremely small (like the charge of an electron: 0.0000000000000000001602 coulombs). Writing out all these zeros is cumbersome and prone to error. Scientific notation solves this problem.

The Scientific Notation Format

A number in scientific notation is written as:

a × 10^b

Where:

  • a = Coefficient (a number greater than or equal to 1, and strictly less than 10)
  • b = Exponent (an integer representing the power of 10)

Scientific Notation Math Rules

When operating on numbers in scientific notation, follow these algebraic rules:

  • Multiplication: Multiply the coefficients and add the exponents.
    (x × 10^a) × (y × 10^b) = (x × y) × 10^(a+b)
  • Division: Divide the coefficients and subtract the exponents.
    (x × 10^a) / (y × 10^b) = (x / y) × 10^(a-b)

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