Scientific+Notation

Scientific Notation is //a method used to write really large or really small numbers in a way that makes them more manageable to use//. For example, it might be difficult or annoying to solve an equation with the number 0.00000000000000099 or 12957000000000000000, so we will write it in scientific notation instead and use or instead.

There is a general format used to write numbers in scientific notation:

__ A number __ x

The number has to be between 1 and 10, which means that we need to have ONLY 1 non-zero digit in front of the decimal point. Since our numbers do not look like this at first, we need to the decimal point from wherever it is originally until there is only 1 non-zero digit in front of it. The number of times we move the decimal point becomes the power.


 * If we have a very small number (a decimal), the power will be negative. If we have a very large number, the power will be positive.


 * Example 1:** Write the number 75,800 in scientific notation.



We have to move the decimal point from the end of the number so that there's only 1 non-zero digit in front of the decimal point. This leaves us with 7.58 (we can leave off any extra zeroes at the end of the number after the decimal point). Since we moved the decimal point 4 times and we started with a large number, we end up with a positive 4 as our exponent.


 * Example 2:** Write 0.000346 in scientific notation.



We move the decimal point so that there is 1 non-zero digit in front of the decimal point and we get 3.46. We had to move the decimal four times from its original place and the number was a decimal, so our exponent is -- 4.

Example 3: Write in standard notation.

-- 0.0000000246

The power (--8) tells us that we have to move the decimal 8 times and the number is going to be a decimal. Therefore, if we move the decimal 8 times to the left and fill in the empty spaces with zeroes, we get our answer.

**TASK: Using what you now know about scientific notation, go back to your flashcards and update your explanation and/or example. If needed, re-write your explanation/definition and add in any important facts that you learned.**

**TASK: Open the document and complete the practice problems. You will need to apply what you already learned about operations with exponents, properties of numbers, and scientific notation in order to solve some of these problems. **