### A good answer might be:

10010 =

    100 div 3 = 33 r 1;
     33 div 3 = 11 r 0;
     11 div 3 =  3 r 2;
      3 div 3 =  1 r 0;
      1 div 3 =  0 r 1

So 10010 = 102013.

# Converting Base 3 to base 7

Checking the answer:

    102013 = 1 × 34 + 0 × 33 + 2 × 32  + 0 × 31 + 1 × 30
           = 1 × 81 + 0 × 27 + 2 × 9 + 0 × 3 + 1
           = 81 + 18 + 1 = 100

To convert from a representation in base three to a representation in base seven, use base ten as an intermediate:

    ____3   ———>    ____10   ———>   ____7

### QUESTION 20:

What is the base 7 representation of 102013?