TEXT: Intermediate Algebra by Miller, O’Neill & Hyde

Videos from Khan Academy.

## What is scientific notation?

Sometimes numbers are too large or small (close to zero) to be comfortably expressed in our usual or **standard **notation. Scientific notation expresses a number as the product of two factors. The first factor captures the most significant digits. The second part, the **magnitude, **is a power of ten, showing us how large or small the number is.

Conversion

To convert a number in standard notation, count the number of times it takes to move the decimal point so that it is just to the right of the first nonzero digit (reading left to right). If the number was large, then the exponent is positive. If the number was small (close to zero), then the exponent is negative.

Examples:

- The main span of the Brooklyn Bridge 19,146 inches. We move the decimal 4 places to the left and since the number is positive, we get 1.9146 x 10^4 inches.
- A student collects a water sample from the foot of the Brooklyn Bridge as part of her project. She looks at the water under a microscope and sees cells of algae that are 0.000026 m by 0.000078 m wide. We move each of the decimal points over 5 places to the right to get. 2.6 x 10^-5 m by 7.8 x 10^-5 m.

Complete the chart on facts regarding the Brooklyn Bridge (from Life and Wikipedia):

Quantity | Standard Notation | Scientific Notation |

car crossings/day (2008) | 123,781 | |

pedestrians opening day | 1.503 x 10^5 | |

total weight of bridge | 29360000 lbs | |

weight of suspended portion | 1.324 x 10^7 lbs | |

length of wires on bridge | 1.406 x 10^4 miles |

Note that the above examples from the bridge all involved large numbers. To get small numbers, let’s go to the world of micro-organisms:

Quantity | Standard Notation | Scientific Notation |

ebola virus | .00000014 m long | |

rhino virus | 2.3 x 10^-8 m diameter |

## Performing operations using scientific notation.

You must be able to in particular multiply and divide. See the videos below:

Pro. Reitz

the video’s for todays lesson help explain scientific notation

This was a great class it was like they hit the refresh button in my brain.

Professor Ezra

The video for today’s lesson help me understand Scientific Notation.

Scientific Notation is a tricky subject: its easy and basic, but then you just make it difficult with the questions. everything that we learn is like smmoshed into one questions and making 10 steps per question just isnt right. I understand the each concept separately but together it kills me.

John

Prof. Reitz

Wow its been a while since i did scientific notation and the lessons and videos refreshed my memory on it 100 %.