5What is Scientific Notation? A short-hand way of writinglarge numbers withoutwriting all of the zeros.
6Why do we use scientific notation? Scientific Notation was developed in order to easily represent numbers that are either very large or very small. Here are two examples of large and small numbers. They are expressed in decimal form instead of scientific notation to help illustrate the problem. The Andromeda Galaxy (the closest major galaxy to our Milky Way galaxy) contains at least 200,000,000,000 stars. On the other hand, the weight of an alpha particle, which is emitted in the radioactive decay of Plutonium-239, is ,000,000,000,000,000,000,000,006,645 kilograms. As you can see, it could get tedious writing out those numbers repeatedly. So, a system was developed to help represent these numbers in a way that was easy to read and understand: Scientific Notation.
7The Distance From the Sun to the Earth The distance of the Earth to the sun is 93,000,000 (93million miles).
8Distance to the Sun in Scientific Notation: Step 1 Move decimal leftLeave only one number in front of decimalExample:93,000,000 =
9Step 2Write number without zerosExample:93,000,000 = 9.3
10Step 3 7 93,000,000 = 9.3 x 10 Count how many places you moved decimal Make that your power of tenExample:93,000,000 = 9.3 x 107
11Practice Problem Standard to Scientific Notation Write in scientific notation.Decide the power of ten.98,500,000 = 9.85 x 10?64,100,000,000 = 6.41 x 10?279,000,000 = 2.79 x 10?4,200,000 = 4.2 x 10?9.85 x 107----->6.41 x 1010----->2.79 x 108----->----->4.2 x 106
12More Practice Problems On these, decide where the decimal will be moved.734,000,000 = ______ x 108870,000,000,000 = ______x 101190,000,000,000 = _____ x 1010Answers3) 9 x 10107.34 x 1082) 8.7 x 1011
13Complete Practice Problems (Start to Finish) Write in scientific notation.50,0007,200,000802,000,000,000Answers1) 5 x 1042) 7.2 x 1063) 8.02 x 1011
14Scientific Notation to Standard Form Move the decimal to the right3.4 x 105 in scientific notationmove the decimal--->340,000 in standard form
15Move the decimal to the right. Write in Standard FormMove the decimal to the right.6.27 x 1069.01 x 1046,270,00090,100