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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