Until now, we have been writing numbers in "decimal notation." Sometimes, especially with large numbers, we need to convert numbers into scientific notation.
To write a number in scientific notation, we write it as a product of a single digit and a power of 10. Here are the steps to writing a number in scientific notation:
Observe: the exponent on "10" corresponds to the number of places that the decimal point has moved--it is positive if the decimal point has moved to the left and negative if it has moved to the right.
One of the trickiest things about scientific notation is remembering the rules for zeros: if a number ends in one or more zeros, do not include the zeros if the number is a whole number, but do include the zeros if the number is a decimal. For example, 820 = 8.2×10^{2} in scientific notation, and 0.820 = 8.20×10^{-1} in scientific notation. Zeros in the middle of a number are treated as normal digits.
Scientific notation makes it easy to compare very large (or very small numbers). The number with a larger exponent on "10" is always greater. For example, 6.7103×10^{13} is greater than 9.2×10^{7} and 8.3×10^{-5} is greater than 2.3×10^{-11} .