 Factorial notation is very simple to use, and has applications in number theory and probability. Factorials work like this: 'Six factorial' is written as 6! using an exclamation sign. It means: 6 x 5 x 4 x 3 x 2 x 1 Factorials are defined for Whole numbers only. The first ten factorials: 1! = 1 2! = 2 x 1 = 2 3! = 3 x 2 x 1 = 6 4! = 4 x 3 x 2 x 1 = 24 5! = 5 x 4 x 3 x 2 x 1 = 120 6! = 6 x 5 x 4 x 3 x 2 x 1 = 720 7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5,040 8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40,320 9! = 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 362,880 10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 3,628,800 As you can see, factorials get pretty large rather quickly. On a phone calculator, the largest factorial you can work out exactly is 18! 18! = 18 x 17 x 16 x ... x 3 x 2 x 1 = 6,402,373,705,728,000 This is because the phone calculator can only display an answer with 16 digits. When you try 19! you will get the answer ; 1.216451004088e17 This means 1.216451004088 x 1017, which is scientific notation. Only 12 decimal places can be shown, so we don't know the rest of them. This makes the answer inexact. To write out the full number, we add zeros for the unknown digits: 1.216451004088 x 1017 = 1.21645100408800000 Such precision isn't often necessary or important, but it is sometimes needed in astronomy, for example, when calculating orbital parameters. |