Scientific Notation

From Department of Mathematics at UTSA
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Scientific notation is a way of expressing numbers that are too large or too small (usually would result in a long string of digits) to be conveniently written in decimal form. The form of a number in scientific notation is , where m is a number with 1 digit in front of the decimal point and k is an integer. For example, 65000000000 is written as in scientific notation, and 0.0000000009 is in scientific notation. To write a number in scientific notation, move the decimal point to be directly after the first (AKA leftmost) nonzero digit. If the decimal was moved n digits to the left, multiply the new number by . If it was moved n digits to the right, multiply by .

Examples:

  • 700: 700 = 700., so we move the decimal point two digits to the left. Thus, 700. = in scientific notation.
  • 0.00051: We need to move the decimal place 4 digits to the right to place it directly after 5, so 0.00051 = in scientific notation.
  • : is approximately 9287, so .


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