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Can someone tell me how bases work? My teacher was teaching them to us and I can't figure it out.

 Jun 14, 2021
 #1
avatar+33757 
+3

Quick review:

Here is how base 10 (decimal) (the one you are familiar with) works

 

345610        Each position is a power of 10    6 is is in the power 0 slot    100 =1      so  6 x 1 = 6

 

                         5 is in the 101   slot    so   5 x 101  = 50

 

                            4 is in the 10slot      4 x 100 = 400

                                 3 is in the 103   slot   so   3000                        added they equal  3000 + 400 + 50 + 6 = 3456

       there are 10 numbers that can be in each slot   0 through 9    for base 10

                  biggest  4 digit base 10 number would be 9999

 

Now here is a base 5 number     1234      numbers in the slots can be anything from 0-4   ( but not 5 ...or 6 or  7 or 8 or 9)

                                                       4 is in the 50 slot    = 4 x 1 = 4

                                                            3 is in the 51   slot =   3 x 5 = 15

                                                                 2 is in the 52 slot  = 2 x 25 = 50

                                                                       1 is in the 53 slot     1 x 125 = 125        added they equal   125 + 50 + 15 + 4 = 19410

                                                                                 biggest four digit base 5 number would be  4444

                             so 12345   = 19410                        Clear as mud?

   

 Jun 14, 2021
edited by ElectricPavlov  Jun 14, 2021
 #2
avatar+114102 
+2
 Jun 18, 2021

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