Exponential Notation Exponential notation is used to express very large or very small numbers.  Space exploration involves very large distances and masses when we talk about planets.  Chemistry and biology involve very large numbers because matter is made up of very small atoms.  For example we could express the speed of light as 300 000 000 m/s or 3.0 X 108 m/s. The second value is much easier to use.  In chemistry a certain  number of molecules is called as mole. It is a very large number because molecules are very small.  The mole represents 602 000 000 000 000 000 000 000 or  6.02 X 1023 molecules. The second value is again much easier to work with. One form of exponential notation commonly used in the sciences is scientific notation.  In scientific notation the number is expressed as a product of a number between 1 and 10 and a power of ten.  The steps by which very large and very small numbers are converted to scientific notation are these: 1. Separate the very large or very small number into two pieces, one of which is the largest factor of ten contained within the number.  For example, the number 50 000 would be separated into two pieces, 5 and 10 000.   10 000 is selected since that is the largest power of ten contained within 50 000. 2. The two pieces are then written as a product, with the second power of ten piece expressed as an exponent.  From the preceding example 50 000 would be 5 and 10 000 which would become 5 and 104  and this would be written as 5 X 104.  10 000 is the same thing as 104. Example_1 Express 350 000 in exponential notation Solution: Step 1:  3.5 X 100 000 Step 2:  3.4 X 105 Example_2 Express 0.000 000 587 in exponential notation Solution Step 1:   5.87 X 0.000 000 1 Step 2:  5.87 X 10-7 Example_3 Write out the number 5.82 X 106 in long form. Solution Step 1:  5.82 X 106 = 5.82 X 1 000 000 Step 2:  5.82 X 1 000 000 = 5 820 000 Example_4 Write out the number 4.92 X 10-5 in long form Solution Step 1:  4.92 X 10-5  =   4.92 X 0.000 01 Step 2:  4.92 X 0.000 01 = 0.000 049 2 Example_5 Find the product of 3.2 X 104 and 6.1 X 102 Solution When multiplying exponential numbers, (1) multiply the first factors by each other, as usual and (2) multiply the exponents by adding the exponents.     3.2 X 104  X 6.1 X 102 =  3.2 X 6.1    X  10(4+2) =  19.52 X 106 =   1.925 X 107 Exponential Notation Practice Level 1 Exponential Notation Practice Level 2 Exponential Notation Practice Level 3