**Scientific notation** is an operation using exponents to write very large and very small numbers. Just like exponents, scientific notation was invented so that we don't have to spend wasted time writing out numbers like (our fingers just cramped typing all those zeros).

Instead we can write this crazy long number as

## Scientific notation has three parts: to it, the coefficient, base, and exponent

**The
coefficient** must be greater than and less than and contain all the
significant digits in the number.

- is not in
scientific notation, since the coefficient is greater than
- Neither is , since the coefficient is less than

**The base** is always

**The exponent** is the number of places the decimal was moved to obtain the coefficient.

## How to Do It

- To get the coefficient, move the decimal to the place after the first "significant digit" in the number. Significant digits are all the non-zero digits in a number. However, if there are zeros in between these numbers, then those zeros are significant, too. Drop all non-significant zeros. We know this sounds confusing. Examples (below) will help, we promise!

- Multiply that by

- To get the exponent, count the number of places you moved the original decimal. This is your exponent.

## Scientific Notation Practice:

Write 26,500,000 in scientific notation. | Note: even if you don't see a decimal at the end of a number, it's there. |

| First, move the decimal behind the 2, so you'll get a number between 1 and 10. Note that it takes 7 jumps to get there. |

| Now drop all non-significant zeros. |

| Multiply this by 10 to the power of 7, since the decimal was
moved seven places. |

Write 307,000 in scientific notation. | This time, there is a zero that is a significant digit. Be sure to include this in the coefficient. |

| Move the decimal until you get a number between 1 and 10 |

| Only drop the three zeros that come after 7. You can't drop the zero that comes before the seven without changing the value of the number. |

| Multiply by 10 to the fifth power, since you moved the decimal five places. |

Write in standard notation. | If scientific notation is shorthand, then **standard notation** is longhand. It's the way you normally write numbers. |

| In this case, since the 10 is raised to the power of 8, move the decimal *eight places to the right* and fill in any blank spots with zeros. |

| |

Write 0.00006009 in scientific notation. | Remember when we told you that you could write very small numbers using scientific notation? Well, here's your big (or really small) chance. |

| Like before, move the decimal until you get a number between 1 and 10. This time, it's five jumps to the right. |

| Drop all of the non-significant zeros. |

| Since we moved the decimal right instead of left this time, the exponent will be negative. Multiply the coefficient by 10 to the power of -5. |

Write in standard notation. | Since the ten is raised to a negative power, you know that you are working with a very small number. |

| Move the decimal 12 places to the left and add zeros in any blank spots. |

| |

Write in scientific notation.

Hint

your coefficient will be 2.004

Answer

Write in standard notation.

Hint

move the decimal 9 places to the right

Answer

Write in scientific notation.

Hint

your exponent will be negative

Answer

Write in standard notation.

Hint

move the decimal to the left

Answer