Difference between revisions of "Scientific Notation"
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* 700: 700 = 700., so we move the decimal point two digits to the left. Thus, 700. = <math> 7.00 * 10^2 </math> in scientific notation. | * 700: 700 = 700., so we move the decimal point two digits to the left. Thus, 700. = <math> 7.00 * 10^2 </math> 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 = <math> 5.1 * 10^{-4} </math> 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 = <math> 5.1 * 10^{-4} </math> in scientific notation. | ||
| − | * <math> | + | * <math> 111\sqrt{7000} </math>: <math> 111\sqrt{7000} </math> is approximately 9287, so <math> 111\sqrt{7000} \approx 9.287 * 10^{3}</math>. |
Revision as of 12:10, 20 September 2021
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 .
Resources
- Exponents and Scientific Notation, OpenStax
- Scientific Notation, Texas A&M University
- Scientific Notation, Math Is Fun
