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Chapter 5.7 Questions 153-158

153. Explain the negative exponent rule and give an example.

The negative exponent rule A-n = 1/an, means that the negative exponent in the numerator is to be switched/moved to the denominator side to be converted into a positive exponent. When there is a negative exponent is gets moved to the numerator and then becomes a positive exponent. You should only move negative exponents.

EX: 5-2= 1/5-2 = 1/25 4x-2 = 4/x-2 X-3/Y-7 = Y7/X3

154. How do you know if an exponential expression is simplified?

The easiest way to know when an exponent is simplified is when the X in the expression has an exponent attached to it.

155. How do you know if a number is written in scientific notation? When you use scientific notation you first need to move the decimal place until you reach a number between 1-10, than you will need to add a power of 10 to show how many places you moved that decimal. '

Example: 2,990,000,000 becomes 2.99 x 109

Being able to really tell when a number is written in scientific notation is when you see that number converted into a decimal times the amount of places of zero where you will see an exponent of 10x how ever many places are left such as the example above.

156. Explain how to convert from scientific to decimal notation and give an example.

When you see a scientific notation and it shows you x 106, the exponent is telling you how many places you need to move. example 4,695 X 106 will turn into 4,695,000. This mean that you need to move the decimal point depending on if the exponent is positive or negative. if the power is negative than you would move the decimal to the left, if positive you would move it to the right. example .000004695.

157. Explain how to convert from decimal to scientific notation and give an example.

To reverse and convert a decimal to scientific notation you will do the opposite. first you will need to count how many times you will need to move the decimal point to make it a number between 1 and 10 and which you would then make that to the power of 10.

Example: .0000023 you will need to move the decimal point 5 places to the right so that you get a number between 1 and 10 making it 2.3 turning your conversation into 2.5x10-5

158. Describe one advantage of expressing a number in scientific notation over decimal notation.
When you have a really large number you still end up with all of the zeros, this can cause problems when working with the numbers because the zeros can be miscounted and or lost. in scientific location you are using the exponent to hold your zeros in a simple and easy form so you can make and equation or number smaller.
Example: 35,000,000,000,000,000,000,000 can be 3521 making this large number smaller. although decimal notation will also give you a smaller number the scientific notation method will make the numbers easier to read and work with.