Scientific Understanding

**What sections should I know before attempting to learn this section?**

—> Exponents

**What is scientific notation?**

Now, we will work on what is called scientific notation. It is a way of representing very large or very small numbers while making them easier and more efficient to write out. For this part of the lesson, you will have to understand the idea of exponents, which I explained earlier in the section exponents.

Scientific notation uses powers of 10. Another way of saying that is scientific notation uses exponents attached to a 10.

**Examples**: Give the regular way to write these scientific notations.

Scientific Notation | Regular Way |

1 * 10^{2} = |
100 |

5 * 10^{-3} = |
.005 |

3.4 * 10^{9} = |
3,400,000,000 |

In the first two examples, there is not a great difference in the amount of time each would require to write and think about. However, the third example is much harder to think about and write out in the regular way, therefore we use scientific notation. Again, just like I explained in the exponents section, the exponent on the 10 is a measure of how many decimal places you move. For the last example, my decimal place started out between the 3 and the 4. I then moved it 9 places to the right and filled in zeros where I had no numbers before. If you want to know how to put scientific notation into a calculator go to this page: **VIDEO how I put this into my calculator**. Knowing how to use your calculator on these will help you check on the answers you are getting in the future.

The other critical thing to realize about scientific notation is that the first number in scientific notation has to be between 1 and 10. Look at example 2 and 3 above. Example 2 is 5 * 10^{-3}. 5 is between 1 and 10. Example 3 is 3.4 * 109. 3.4 is between 1 and 10.

We can now try some examples together to help us get the hang of this concept. First, we will try to take a scientific notation and produce the number in the usual way you view it.

**VIDEO Scientific Notation Demonstrated Example 1**: Write out the number below in non-scientific notation form.

2.6 * 10^{-4}

Where do we start?

Answer: Write down 2.6

What do we look at next?

Answer: The exponent on the 10

Is the exponent negative or positive?

Answer: Negative

What does that mean?

Answer: It means we have to move the decimal left

How many places do we have to move the decimal left?

Answer: 4 (because that is the number in the exponent)

What does it look like after I move the decimal 4 spots to the left?

COMPLETE ANSWER: 0.00026

**VIDEO Scientific Notation Demonstrated Example 2**: Write out the number below in non-scientific notation form.

1.7 * 10^{6}

Where do we start?

Answer: Write down 1.7

What do we look at next?

Answer: The exponent on the 10

Is the exponent negative or positive?

Answer: Positive

What does that mean?

Answer: It means we have to move the decimal right.

How many places do we have to move the decimal right?

Answer: 6 (because that is the number in the exponent)

What does it look like after I move the decimal 6 spots to the right?

COMPLETE ANSWER: 1,700,000

**PRACTICE PROBLEMS**: Write out the number in non-scientific notation form.

6.3 * 10^{3} |
6300 |

9.5 * 10^{-4} |
0.00095 |

2.48 * 10^{-8} |
0.0000000248 |

1.678923 * 10^{4} |
16789.23 |

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