Scientific Notation .k12.ga.us
Scientific Notation | |
| | Scientific notation is simply a method for expressing, and working with, very large or very small numbers. It is a short hand |
| |method for writing numbers, and an easy method for calculations. Numbers in scientific notation are made up of three parts: the |
| |coefficient, the base and the exponent. Observe the example below: |
| |5.67 x 105 |
| |This is the scientific notation for the standard number, 567 000. Now look at the number again, with the three parts labeled. |
| |5.67 x 105 |
| | coefficient base exponent |
| | |
| | In order for a number to be in correct scientific notation, the following conditions must be true: |
| |1. The coefficient must be greater than or equal to 1 and less than 10. |
| |2. The base must be 10. |
| |3. The exponent must show the number of decimal places that the decimal needs to be moved to change the number to standard notation. A |
| |negative exponent means that the decimal is moved to the left when changing to standard notation. |
| |[pic] |
| |Changing numbers from scientific notation to standard notation. |
| | Ex.1 Change 6.03 x 107 to standard notation. |
| |remember, 107 = 10 x 10 x 10 x 10 x 10 x 10 x 10 = 10 000 000 |
| |so, 6.03 x 107 = 6.03 x 10 000 000 = 60 300 000 |
| |answer = 60 300 000 |
| |Instead of finding the value of the base, we can simply move the decimal seven places to the right because the exponent is 7. |
| |So, 6.03 x 107 = 60 300 000 |
| |[pic] |
| |Now let us try one with a negative exponent. |
| |Ex.2 Change 5.3 x 10-4 to standard notation. |
| |The exponent tells us to move the decimal four places to the left. |
| |so, 5.3 x 10-4 = 0.00053 |
| |[pic] |
| |Changing numbers from standard notation to scientific notation |
| |Ex.1 Change 56 760 000 000 to scientific notation |
| |Remember, the decimal is at the end of the final zero. |
| |The decimal must be moved behind the five to ensure that the coefficient is less than 10, but greater than or equal to one. |
| |The coefficient will then read 5.676 |
| |The decimal will move 10 places to the left, making the exponent equal to 10. |
| |Answer equals 5.676 x 1010 |
| |[pic] |
| |Now we try a number that is very small. |
| |Ex.2 Change 0.000000902 to scientific notation |
| |The decimal must be moved behind the 9 to ensure a proper coefficient. |
| |The coefficient will be 9.02 |
| |The decimal moves seven spaces to the right, making the exponent -7 |
| |Answer equals 9.02 x 10-7 |
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